| Title: | Probabilistic Hazard Assessment |
|---|---|
| Description: | Computes the probability density and cumulative distribution functions of fourteen distributions used for the probabilistic hazard assessment. Estimates the model parameters of the distributions using the maximum likelihood and reports the goodness-of-fit statistics. The recurrence interval estimations of earthquakes are computed for each distribution. |
| Authors: | Emrah Altun [aut, cre, cph], Gamze Ozel [ctb] |
| Maintainer: | Emrah Altun <[email protected]> |
| License: | GPL-3 |
| Version: | 0.1.0 |
| Built: | 2025-02-14 05:26:12 UTC |
| Source: | https://github.com/cran/ERPeq |
Cumulative distribution function of the Birnbaum-Saunders-Generalized Pareto distribution
cdfbsgdp(par, x)cdfbsgdp(par, x)
par |
parameter vector of the Birnbaum-Saunders-Generalized Pareto distribution. First parameter is the shape, second parameter is the scale parameter. Third parameter is the lower bound parameter. |
x |
vector of observations or single value |
return the value of the cdf of the Birnbaum-Saunders-Generalized Pareto distribution
Altun, E., Ozel, G. A novel approach to probabilistic hazard assessment: BSGPD model. (Under Review)
cdfbsgdp(c(0.5,2,0.5),3)cdfbsgdp(c(0.5,2,0.5),3)
Cumulative distribution function of the exponentiated exponential distribution
cdfeexp(par, x)cdfeexp(par, x)
par |
parameter vector of the exponentiated exponential distribution. First parameter is the shape, second is the scale parameter. |
x |
vector of observations or single value |
return the value of the pdf of the exponentiated exponential distribution
Gupta, R. D., & Kundu, D. (1999). Theory & methods: Generalized exponential distributions. Australian & New Zealand Journal of Statistics, 41(2), 173-188.
cdfeexp(c(0.5,0.3),2)cdfeexp(c(0.5,0.3),2)
Cumulative distribution function of the exponentiated Rayleigh distribution
cdfer(par, x)cdfer(par, x)
par |
parameter vector of the exponentiated Rayleigh distribution. First parameter is the scale, second is the shape parameter. |
x |
vector of observations or single value |
return the value of the pdf of the exponentiated Rayleigh distribution
Vodă, V. G. (1976). Inferential procedures on a generalized Rayleigh variate. I. Aplikace matematiky, 21(6), 395-412.
cdfer(c(0.5,0.3),2)cdfer(c(0.5,0.3),2)
Cumulative distribution function of the exponentiated Weibull distribution
cdfew(par, x)cdfew(par, x)
par |
parameter vector of the exponentiated Weibull distribution. First parameter is the shape, second is the scale parameter and third parameter is shape parameter. |
x |
vector of observations or single value |
return the value of the pdf of the exponentiated Weibull distribution
Mudholkar, G. S., & Srivastava, D. K. (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE transactions on reliability, 42(2), 299-302.
cdfew(c(0.5,0.3,0.6),2)cdfew(c(0.5,0.3,0.6),2)
Cumulative distribution function of the Gamma distribution
cdfgamma(par, x)cdfgamma(par, x)
par |
parameter vector of the gamma distribution. First parameter is the shape and second is the scale parameter |
x |
vector of quantiles |
return the value of the cdf of the gamma distribution
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 21. Wiley, New York.
cdfgamma(c(2,3),5)cdfgamma(c(2,3),5)
Cumulative distribution function of the generalized gamma distribution
cdfggamma(par, x)cdfggamma(par, x)
par |
parameter vector of the generalized gamma distribution. First parameter is the dispersion, second is the location parameter and third is the family parameter. |
x |
vector of observations or single value |
return the value of the pdf of the generalized gamma distribution
Stacy, E. W. (1962). A generalization of the gamma distribution. The Annals of mathematical statistics, 1187-1192.
pdfggamma(c(2,5,3),3)pdfggamma(c(2,5,3),3)
Cumulative distribution function of the gumbel distribution
cdfgumbel(par, x)cdfgumbel(par, x)
par |
parameter vector of the gumbel distribution. First parameter is the location, second is the scale parameter. |
x |
vector of observations or single value |
return the value of the pdf of the gumbel distribution
Gumbel, E. J. (1941). The return period of flood flows. The annals of mathematical statistics, 12(2), 163-190.
pdfgumbel(c(0.5,0.3),2)pdfgumbel(c(0.5,0.3),2)
Cumulative distribution function of the inverse gamma distribution
cdfinvgamma(par, x)cdfinvgamma(par, x)
par |
parameter vector of the inverse gamma distribution. First parameter is the shape, second is the rate parameter. |
x |
vector of observations or single value |
return the value of the pdf of the inverse gamma distribution
Cook, J. D. (2008). Inverse gamma distribution. online: http://www. johndcook. com/inverse gamma. pdf, Tech. Rep.
cdfinvgamma(c(2,5,3),3)cdfinvgamma(c(2,5,3),3)
Cumulative distribution function of the inverse Weibull distribution
cdfiwweibull(par, x)cdfiwweibull(par, x)
par |
parameter vector of the inverse Weibull distribution. First parameter is the shape and second is the scale parameter |
x |
vector of quantiles |
return the value of the cdf of the inverse Weibull distribution
Mudholkar, G. S., & Kollia, G. D. (1994). Generalized Weibull family: a structural analysis. Communications in statistics-theory and methods, 23(4), 1149-1171.
cdfiwweibull(c(2,3),5)cdfiwweibull(c(2,3),5)
Cumulative distribution function of the Levy distribution
cdflevy(par, x)cdflevy(par, x)
par |
parameter vector of the Levy distribution. First parameter is the location, second is the scale parameter. |
x |
vector of observations or single value |
return the value of the pdf of the Levy distribution
Nolan, J. P. (2003). Modeling financial data with stable distributions. In Handbook of heavy tailed distributions in finance (pp. 105-130). North-Holland.
cdflevy(c(0.5,0.3),2)cdflevy(c(0.5,0.3),2)
Cumulative distribution function of the log-normal distribution
cdflnormal(par, x)cdflnormal(par, x)
par |
parameter vector of the log-normal distribution. First parameter is the shape and second is the scale parameter |
x |
vector of quantiles |
return the value of the cdf of the log-normal distribution
Heyde, C. C. (1963). On a property of the lognormal distribution. Journal of the Royal Statistical Society: Series B (Methodological), 25(2), 392-393.
cdflnormal(c(2,3),5)cdflnormal(c(2,3),5)
Cumulative distribution function of the Pareto distribution
cdfpareto(par, x)cdfpareto(par, x)
par |
parameter vector of the Pareto distribution. First parameter is the shape and second is the scale parameter |
x |
vector of quantiles |
return the value of the cdf of the Pareto distribution
Arnold, B. C. (1983). Pareto Distributions, International Cooperative Publishing House.
cdfpareto(c(2,5),2)cdfpareto(c(2,5),2)
Cumulative distribution function of the Rayleigh distribution
cdfrayleigh(par, x)cdfrayleigh(par, x)
par |
scale parameter vector of the Rayleigh distribution. |
x |
vector of quantiles |
return the value of the cdf of the Rayleigh distribution
Siddiqui, M. M. (1964). Statistical inference for Rayleigh distributions. Journal of Research of the National Bureau of Standards, Sec. D, 68(9), 1005-1010.
cdfrayleigh(c(2),5)cdfrayleigh(c(2),5)
Cumulative distribution function of the Weibull distribution
cdfweibull(par, x)cdfweibull(par, x)
par |
parameter vector of the Weibull distribution. First parameter is the shape and second is the scale parameter |
x |
vector of quantiles |
return the value of the cdf of the weibull distribution
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 21. Wiley, New York.
cdfweibull(c(2,3),5)cdfweibull(c(2,3),5)
The elapsed time (year) between the earthquakes with 6 and 6.5 magnitudes in Turkey occured between the years of 1990-2021
data_earthquake_6_6.5data_earthquake_6_6.5
A numeric vector
The elapsed time (year) between the earthquakes with 6.5 and 7 magnitudes in Turkey occured between the years of 1990-2021
data_earthquake_6.5_7data_earthquake_6.5_7
A numeric vector
The elapsed time (year) between the earthquakes having the magnitudes higher than 7 in Turkey occured between the years of 1990-2021
data_earthquake_7data_earthquake_7
A numeric vector
Computes the probability of an earthquake within a specified time "r" and elapsed time "te".
expexpcp(fit, r, te)expexpcp(fit, r, te)
fit |
Fit is the fitexpexp object. See ?fitexpexp for details. |
r |
The specified time in which the probability of an earthquake is desired to be calculated. |
te |
Elapsed time since the last earthquake |
A numeric value
Pasari, S. and Dikshit, O. (2014). Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure and Applied Geophysics, 171, 1251-1281.
fit=fitexpexp(c(1,1),data=data_earthquake_7) expexpcp(fit,r=2,te=5)fit=fitexpexp(c(1,1),data=data_earthquake_7) expexpcp(fit,r=2,te=5)
Computes the probability of an earthquake within a specified time "r" and elapsed time "te".
expraycp(fit, r, te)expraycp(fit, r, te)
fit |
Fit is the fitexprayleigh object. See ?fitexprayleigh for details. |
r |
The specified time in which the probability of an earthquake is desired to be calculated. |
te |
Elapsed time since the last earthquake |
A numeric value
Pasari, S. and Dikshit, O. (2014). Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure and Applied Geophysics, 171, 1251-1281.
fit=fitexprayleigh(c(0.5,0.5),data=data_earthquake_7) expraycp(fit,r=2,te=5)fit=fitexprayleigh(c(0.5,0.5),data=data_earthquake_7) expraycp(fit,r=2,te=5)
Computes the probability of an earthquake within a specified time "r" and elapsed time "te".
expweicp(fit, r, te)expweicp(fit, r, te)
fit |
Fit is the fitexpweibull object. See ?fitexpweibull for details. |
r |
The specified time in which the probability of an earthquake is desired to be calculated. |
te |
Elapsed time since the last earthquake |
A numeric value
Pasari, S. and Dikshit, O. (2014). Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure and Applied Geophysics, 171, 1251-1281.
fit=fitexpweibull(c(1,1,1),data=data_earthquake_7) expweicp(fit,r=2,te=5)fit=fitexpweibull(c(1,1,1),data=data_earthquake_7) expweicp(fit,r=2,te=5)
Fitting the Birnbaum-Saunders-Generalized Pareto distribution
fitbsgpd(starts, data)fitbsgpd(starts, data)
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
library(VGAM) data=ERPeq::rbsgpd(500,5,0.7,0.2) fitbsgpd(starts =c(1,1),data=data)library(VGAM) data=ERPeq::rbsgpd(500,5,0.7,0.2) fitbsgpd(starts =c(1,1),data=data)
Fitting the exponentiated exponential distribution
fitexpexp(starts, data)fitexpexp(starts, data)
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
data=rexpexp(500,2,3) fitexpexp(starts =c(2,2),data=data)data=rexpexp(500,2,3) fitexpexp(starts =c(2,2),data=data)
Fitting the exponentiated exponentiated Rayleigh distribution
fitexprayleigh(starts, data)fitexprayleigh(starts, data)
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
data=rexprayleigh(500,2,3) fitexprayleigh(starts =c(2,2),data=data)data=rexprayleigh(500,2,3) fitexprayleigh(starts =c(2,2),data=data)
Fitting the exponentiated Weibull distribution
fitexpweibull(starts, data)fitexpweibull(starts, data)
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
data=rexpweibull(500,2,3,5) fitexpweibull(starts =c(2,2,2),data=data)data=rexpweibull(500,2,3,5) fitexpweibull(starts =c(2,2,2),data=data)
Fitting the gamma distribution
fitgamma(starts, data)fitgamma(starts, data)
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
datagamma=rgamma(500,2,2) fitgamma(starts =c(2,2),data=datagamma)datagamma=rgamma(500,2,2) fitgamma(starts =c(2,2),data=datagamma)
Fitting the generalized gamma distribution
fitggamma(starts, data)fitggamma(starts, data)
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
library(rmutil) data=rggamma(500,2,2,2) fitggamma(starts =c(1,1,1),data=data)library(rmutil) data=rggamma(500,2,2,2) fitggamma(starts =c(1,1,1),data=data)
Fitting the Gumbel distribution
fitgumbel(starts, data)fitgumbel(starts, data)
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
library(VGAM) data=rgumbel(500,2,0.5) fitgumbel(starts =c(2,2),data=data)library(VGAM) data=rgumbel(500,2,0.5) fitgumbel(starts =c(2,2),data=data)
Fitting the inverse gamma distribution
fitinvgamma(starts, data)fitinvgamma(starts, data)
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
library(invgamma) data=rinvgamma(500,2,0.5) fitinvgamma(starts =c(2,2),data=data)library(invgamma) data=rinvgamma(500,2,0.5) fitinvgamma(starts =c(2,2),data=data)
Fitting the gamma distribution
fitiweibull(starts, data)fitiweibull(starts, data)
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
set.seed(7) data=rgamma(500,shape=1,scale=1) fitiweibull(starts =c(0.5,0.5),data=data)set.seed(7) data=rgamma(500,shape=1,scale=1) fitiweibull(starts =c(0.5,0.5),data=data)
Fitting the Levy distribution
fitlevy(starts, data)fitlevy(starts, data)
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
library(VGAM) data=ERPeq::rlevy(100,2,0.1) fitlevy(starts =c(0.1),data=data)library(VGAM) data=ERPeq::rlevy(100,2,0.1) fitlevy(starts =c(0.1),data=data)
Fitting the log-normal distribution
fitlnormal(starts, data)fitlnormal(starts, data)
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
data=rlnorm(500,2,0.5) fitlnormal(starts =c(2,2),data=data)data=rlnorm(500,2,0.5) fitlnormal(starts =c(2,2),data=data)
Fitting the Pareto distribution
fitpareto(starts, data)fitpareto(starts, data)
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
library(VGAM) data=VGAM::rpareto(500,5,2) fitpareto(starts =c(2),data=data)library(VGAM) data=VGAM::rpareto(500,5,2) fitpareto(starts =c(2),data=data)
Fitting the Rayleigh distribution
fitrayleigh(starts, data)fitrayleigh(starts, data)
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
library(VGAM) data=rrayleigh(500,2) fitrayleigh(starts =c(2),data=data)library(VGAM) data=rrayleigh(500,2) fitrayleigh(starts =c(2),data=data)
Fitting the Weibull distribution
fitweibull(starts, data)fitweibull(starts, data)
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
dataweibull=rweibull(500,2,2) fitweibull(starts =c(2,2),data=dataweibull)dataweibull=rweibull(500,2,2) fitweibull(starts =c(2,2),data=dataweibull)
Computes the probability of an earthquake within a specified time "r" and elapsed time "te".
gammacp(fit, r, te)gammacp(fit, r, te)
fit |
Fit is the fitgamma object. See ?fitgamma for details. |
r |
The specified time in which the probability of an earthquake is desired to be calculated. |
te |
Elapsed time since the last earthquake |
A numeric value
Pasari, S. and Dikshit, O. (2014). Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure and Applied Geophysics, 171, 1251-1281.
fit=fitgamma(c(1,1),data=data_earthquake_6_6.5) gammacp(fit,r=2,te=5)fit=fitgamma(c(1,1),data=data_earthquake_6_6.5) gammacp(fit,r=2,te=5)
Computes the probability of an earthquake within a specified time "r" and elapsed time "te".
ggammacp(fit, r, te)ggammacp(fit, r, te)
fit |
Fit is the fitggamma object. See ?fitggamma for details. |
r |
The specified time in which the probability of an earthquake is desired to be calculated. |
te |
Elapsed time since the last earthquake |
A numeric value
Pasari, S. and Dikshit, O. (2014). Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure and Applied Geophysics, 171, 1251-1281.
fit=fitggamma(c(1,1,1),data=data_earthquake_6_6.5) ggammacp(fit,r=2,te=5)fit=fitggamma(c(1,1,1),data=data_earthquake_6_6.5) ggammacp(fit,r=2,te=5)
Computes the probability of an earthquake within a specified time "r" and elapsed time "te".
gumbelcp(fit, r, te)gumbelcp(fit, r, te)
fit |
Fit is the fitgumbel object. See ?fitgumbel for details. |
r |
The specified time in which the probability of an earthquake is desired to be calculated. |
te |
Elapsed time since the last earthquake |
A numeric value
Pasari, S. and Dikshit, O. (2014). Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure and Applied Geophysics, 171, 1251-1281.
fit=fitgumbel(c(1,1),data=data_earthquake_7) gumbelcp(fit,r=2,te=5)fit=fitgumbel(c(1,1),data=data_earthquake_7) gumbelcp(fit,r=2,te=5)
Computes the probability of an earthquake within a specified time "r" and elapsed time "te".
invgammacp(fit, r, te)invgammacp(fit, r, te)
fit |
Fit is the fitinvgamma object. See ?fitinvgamma for details. |
r |
The specified time in which the probability of an earthquake is desired to be calculated. |
te |
Elapsed time since the last earthquake |
A numeric value
Pasari, S. and Dikshit, O. (2014). Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure and Applied Geophysics, 171, 1251-1281.
fit=fitinvgamma(c(1,1),data=data_earthquake_7) invgammacp(fit,r=2,te=5)fit=fitinvgamma(c(1,1),data=data_earthquake_7) invgammacp(fit,r=2,te=5)
Computes the probability of an earthquake within a specified time "r" and elapsed time "te".
iweibullcp(fit, r, te)iweibullcp(fit, r, te)
fit |
Fit is the fitiwebull object. See ?fitiwebull for details. |
r |
The specified time in which the probability of an earthquake is desired to be calculated. |
te |
Elapsed time since the last earthquake |
A numeric value
Pasari, S. and Dikshit, O. (2014). Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure and Applied Geophysics, 171, 1251-1281.
fit=fitiweibull(c(1,1),data=data_earthquake_6.5_7) iweibullcp(fit,r=2,te=5)fit=fitiweibull(c(1,1),data=data_earthquake_6.5_7) iweibullcp(fit,r=2,te=5)
Computes the probability of an earthquake within a specified time "r" and elapsed time "te".
levycp(fit, r, te)levycp(fit, r, te)
fit |
Fit is the fitlevy object. See ?fitlevy for details. |
r |
The specified time in which the probability of an earthquake is desired to be calculated. |
te |
Elapsed time since the last earthquake |
A numeric value
Pasari, S. and Dikshit, O. (2014). Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure and Applied Geophysics, 171, 1251-1281.
fit=fitlevy(c(1),data=data_earthquake_7) levycp(fit,r=2,te=5)fit=fitlevy(c(1),data=data_earthquake_7) levycp(fit,r=2,te=5)
Computes the probability of an earthquake within a specified time "r" and elapsed time "te".
lnormalcp(fit, r, te)lnormalcp(fit, r, te)
fit |
Fit is the fitlnormal object. See ?fitlnormal for details. |
r |
The specified time in which the probability of an earthquake is desired to be calculated. |
te |
Elapsed time since the last earthquake |
A numeric value
Pasari, S. and Dikshit, O. (2014). Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure and Applied Geophysics, 171, 1251-1281.
fit=fitlnormal(c(1,1),data=data_earthquake_6.5_7) lnormalcp(fit,r=2,te=5)fit=fitlnormal(c(1,1),data=data_earthquake_6.5_7) lnormalcp(fit,r=2,te=5)
Computes the probability of an earthquake within a specified time "r" and elapsed time "te".
paretocp(fit, r, te)paretocp(fit, r, te)
fit |
Fit is the fitpareto object. See ?fitpareto for details. |
r |
The specified time in which the probability of an earthquake is desired to be calculated. |
te |
Elapsed time since the last earthquake |
A numeric value
Pasari, S. and Dikshit, O. (2014). Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure and Applied Geophysics, 171, 1251-1281.
library(VGAM) data=VGAM::rpareto(200,2,5) fit=fitpareto(c(0.5),data=data) paretocp(fit,r=2,te=5)library(VGAM) data=VGAM::rpareto(200,2,5) fit=fitpareto(c(0.5),data=data) paretocp(fit,r=2,te=5)
Probability density function of the Birnbaum-Saunders-Generalized Pareto distribution
pdfbsgdp(par, x)pdfbsgdp(par, x)
par |
parameter vector of the Birnbaum-Saunders-Generalized Pareto distribution. First parameter is the shape, second parameter is the scale parameter. Third parameter is the lower bound parameter. |
x |
vector of observations or single value |
return the value of the pdf of the Birnbaum-Saunders-Generalized Pareto distribution.
Altun, E., Ozel, G. A novel approach to probabilistic hazard assessment: BSGPD model. (Under Review)
pdfbsgdp(c(2,0.5,0.5),1)pdfbsgdp(c(2,0.5,0.5),1)
Probability density function of the exponentiated exponential distribution
pdfeexp(par, x)pdfeexp(par, x)
par |
parameter vector of the exponentiated exponential distribution. First parameter is the shape, second is the scale parameter. |
x |
vector of observations or single value |
return the value of the pdf of the exponentiated exponential distribution
Gupta, R. D., & Kundu, D. (1999). Theory & methods: Generalized exponential distributions. Australian & New Zealand Journal of Statistics, 41(2), 173-188. Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 21. Wiley, New York.
pdfeexp(c(0.5,0.3),2)pdfeexp(c(0.5,0.3),2)
Probability density function of the exponentiated Rayleigh distribution
pdfer(par, x)pdfer(par, x)
par |
parameter vector of the exponentiated Rayleigh distribution. First parameter is the scale, second is the shape parameter. |
x |
vector of observations or single value |
return the value of the pdf of the exponentiated Rayleigh distribution
Vodă, V. G. (1976). Inferential procedures on a generalized Rayleigh variate. I. Aplikace matematiky, 21(6), 395-412.
pdfer(c(0.5,0.3),2)pdfer(c(0.5,0.3),2)
Probability density function of the exponentiated Weibull distribution
pdfew(par, x)pdfew(par, x)
par |
parameter vector of the exponentiated Weibull distribution. First parameter is the shape, second is the scale parameter and third parameter is shape parameter. |
x |
vector of observations or single value |
return the value of the pdf of the exponentiated Weibull distribution
Mudholkar, G. S., & Srivastava, D. K. (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE transactions on reliability, 42(2), 299-302.
pdfew(c(0.5,0.3,0.6),2)pdfew(c(0.5,0.3,0.6),2)
Probability density function of the Gamma distribution
pdfgamma(par, x)pdfgamma(par, x)
par |
parameter vector of the gamma distribution. First parameter is the shape and second is the scale parameter |
x |
vector of observations or single value |
return the value of the pdf of the gamma distribution
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 21. Wiley, New York.
pdfgamma(c(2,3),5)pdfgamma(c(2,3),5)
Probability density function of the generalized gamma distribution
pdfggamma(par, x)pdfggamma(par, x)
par |
parameter vector of the generalized gamma distribution. First parameter is the dispersion, second is the location parameter and third is the family parameter. |
x |
vector of observations or single value |
return the value of the pdf of the generalized gamma distribution
Stacy, E. W. (1962). A generalization of the gamma distribution. The Annals of mathematical statistics, 1187-1192.
pdfggamma(c(2,5,3),3)pdfggamma(c(2,5,3),3)
Probability density function of the gumbel distribution
pdfgumbel(par, x)pdfgumbel(par, x)
par |
parameter vector of the gumbel distribution. First parameter is the location, second is the scale parameter. |
x |
vector of observations or single value |
return the value of the pdf of the gumbel distribution
Gumbel, E. J. (1941). The return period of flood flows. The annals of mathematical statistics, 12(2), 163-190.
pdfgumbel(c(0.5,0.3),2)pdfgumbel(c(0.5,0.3),2)
Probability density function of the inverse gamma distribution
pdfinvgamma(par, x)pdfinvgamma(par, x)
par |
parameter vector of the inverse gamma distribution. First parameter is the shape, second is the rate parameter. |
x |
vector of observations or single value |
return the value of the pdf of the inverse gamma distribution
Cook, J. D. (2008). Inverse gamma distribution. online: http://www. johndcook. com/inverse gamma. pdf, Tech. Rep.
pdfinvgamma(c(2,5,3),3)pdfinvgamma(c(2,5,3),3)
Probability density function of the inverse Weibull distribution
pdfiweibull(par, x)pdfiweibull(par, x)
par |
parameter vector of the inverse Weibull distribution. First parameter is the shape and second is the scale parameter |
x |
vector of observations or single value |
return the value of the pdf of the inverse Weibull distribution
Mudholkar, G. S., & Kollia, G. D. (1994). Generalized Weibull family: a structural analysis. Communications in statistics-theory and methods, 23(4), 1149-1171.
pdfiweibull(c(2,3),5)pdfiweibull(c(2,3),5)
Probability density function of the Levy distribution
pdflevy(par, x)pdflevy(par, x)
par |
parameter vector of the Levy distribution. First parameter is the location, second is the scale parameter. |
x |
vector of observations or single value |
return the value of the pdf of the Levy distribution
Nolan, J. P. (2003). Modeling financial data with stable distributions. In Handbook of heavy tailed distributions in finance (pp. 105-130). North-Holland.
pdflevy(c(0.5,0.3),2)pdflevy(c(0.5,0.3),2)
Probability density function of the log-normal distribution
pdflnormal(par, x)pdflnormal(par, x)
par |
parameter vector of the log-normal distribution. First parameter is the shape and second is the scale parameter |
x |
vector of observations or single value |
return the value of the pdf of the log-normal distribution
Heyde, C. C. (1963). On a property of the lognormal distribution. Journal of the Royal Statistical Society: Series B (Methodological), 25(2), 392-393.
pdflnormal(c(2,3),5)pdflnormal(c(2,3),5)
Probability density function of the Pareto distribution
pdfpareto(par, x)pdfpareto(par, x)
par |
parameter vector of the Pareto distribution. First parameter is the scale and second is the shape parameter |
x |
vector of observations or single value |
return the value of the pdf of the Pareto distribution
Arnold, B. C. (1983). Pareto Distributions, International Cooperative Publishing House.
pdfpareto(c(2,5),3)pdfpareto(c(2,5),3)
Probability density function of the Rayleigh distribution
pdfrayleigh(par, x)pdfrayleigh(par, x)
par |
scale parameter vector of the Rayleigh distribution. |
x |
vector of observations or single value |
return the value of the pdf of the Rayleigh distribution
Siddiqui, M. M. (1964). Statistical inference for Rayleigh distributions. Journal of Research of the National Bureau of Standards, Sec. D, 68(9), 1005-1010.
pdfrayleigh(c(2),5)pdfrayleigh(c(2),5)
Probability density function of the Weibull distribution
pdfweibull(par, x)pdfweibull(par, x)
par |
parameter vector of the weibull distribution. First parameter is the shape and second is the scale parameter |
x |
vector of observations or single value |
return the value of the pdf of the weibull distribution
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 21. Wiley, New York.
pdfweibull(c(2,3),5)pdfweibull(c(2,3),5)
Computes the probability of an earthquake within a specified time "r" and elapsed time "te".
rayleighcp(fit, r, te)rayleighcp(fit, r, te)
fit |
Fit is the fitrayleigh object. See ?fitrayleigh for details. |
r |
The specified time in which the probability of an earthquake is desired to be calculated. |
te |
Elapsed time since the last earthquake |
A numeric value
Pasari, S. and Dikshit, O. (2014). Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure and Applied Geophysics, 171, 1251-1281.
fit=fitrayleigh(c(1),data=data_earthquake_7) rayleighcp(fit,r=2,te=5)fit=fitrayleigh(c(1),data=data_earthquake_7) rayleighcp(fit,r=2,te=5)
Generate random observations from Birnbaum-Saunders-Generalized Pareto distribution
rbsgpd(n, beta, alpha, gamma)rbsgpd(n, beta, alpha, gamma)
n |
number of observations to be generated from the Birnbaum-Saunders-Generalized Pareto |
beta |
lower bound parameter of the |
alpha |
scale parameter of the Birnbaum-Saunders-Generalized Pareto distribution |
gamma |
shape parameter of the Birnbaum-Saunders-Generalized Pareto distribution |
return the random sample generated from scale parameter of the Birnbaum-Saunders-Generalized Pareto distribution distribution
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 21. Wiley, New York.
rbsgpd(100,2,3,5)rbsgpd(100,2,3,5)
Generate random observations from exponentiated exponential distribution
rexpexp(n, alpha, lambda)rexpexp(n, alpha, lambda)
n |
number of observations to be generated |
alpha |
shape parameter of the exponentiated exponential distribution |
lambda |
scale parameter of the exponentiated exponential distribution |
return the random sample generated from exponentiated exponential distribution
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 21. Wiley, New York.
rexpexp(100,2,3)rexpexp(100,2,3)
Generate random observations from exponentiated Rayleigh distribution
rexprayleigh(n, alpha, beta)rexprayleigh(n, alpha, beta)
n |
number of observations to be generated |
alpha |
shape parameter of the exponentiated Rayleigh distribution |
beta |
scale parameter of the exponentiated Rayleigh distribution |
return the random sample generated from exponentiated exponential distribution
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 21. Wiley, New York.
rexprayleigh(100,2,3)rexprayleigh(100,2,3)
Generate random observations from exponentiated Weibull distribution
rexpweibull(n, alpha, beta, theta)rexpweibull(n, alpha, beta, theta)
n |
number of observations to be generated |
alpha |
shape parameter of the exponentiated Weibull distribution |
beta |
scale parameter of the exponentiated Weibull distribution |
theta |
shape parameter of the exponentiated Weibull distribution |
return the random sample generated from exponentiated Weibull distribution
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 21. Wiley, New York.
rexpweibull(100,2,3,2)rexpweibull(100,2,3,2)
Generate random observations from Levy distribution
rlevy(n, mu, c)rlevy(n, mu, c)
n |
number of observations to be generated |
mu |
location parameter of the Levy distribution |
c |
scale parameter of the Levy distribution |
return the random sample generated from Levy distribution
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 21. Wiley, New York.
rlevy(500,2,3)rlevy(500,2,3)
Computes the probability of an earthquake within a specified time "r" and elapsed time "te".
weibullcp(fit, r, te)weibullcp(fit, r, te)
fit |
Fit is the fitweibull object. See ?fitweibull for details. |
r |
The specified time in which the probability of an earthquake is desired to be calculated. |
te |
Elapsed time since the last earthquake |
A numeric value
Pasari, S. and Dikshit, O. (2014). Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure and Applied Geophysics, 171, 1251-1281.
fit=fitweibull(c(1,1),data=data_earthquake_6_6.5) weibullcp(fit,r=2,te=5)fit=fitweibull(c(1,1),data=data_earthquake_6_6.5) weibullcp(fit,r=2,te=5)