Package invgamma. May 7, 2017
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1 Package invgamma May 7, 2017 Type Package Title The Inverse Gamma Distribution Version 1.1 URL BugReports Description Light weight implementation of the standard distribution functions for the inverse gamma distribution, wrapping those for the gamma distribution in the stats package. License GPL-2 RoxygenNote NeedsCompilation no Author David Kahle [aut, cre, cph], James Stamey [aut, cph] Maintainer David Kahle Repository CRAN Date/Publication :22:52 UTC R topics documented: invchisq invexp invgamma Index 6 1
2 2 invchisq invchisq The Inverse (non-central) Chi-Squared Distribution Description Usage Density, distribution function, quantile function and random generation for the inverse chi-squared distribution. dinvchisq(x, df, ncp = 0, log = FALSE) pinvchisq(q, df, ncp = 0, lower.tail = TRUE, log.p = FALSE) qinvchisq(p, df, ncp = 0, lower.tail = TRUE, log.p = FALSE) rinvchisq(n, df, ncp = 0) Arguments x, q vector of quantiles. df ncp log, log.p lower.tail p n Details degrees of freedom (non-negative, but can be non-integer). non-centrality parameter (non-negative). logical; if TRUE, probabilities p are given as log(p). logical; if TRUE (default), probabilities are P[X <= x] otherwise, P[X > x]. vector of probabilities. number of observations. If length(n) > 1, the length is taken to be the number required. The functions (d/p/q/r)invchisq simply wrap those of the standard (d/p/q/r)chisq R implementation, so look at, say, dchisq for details. See Also dchisq; these functions just wrap the (d/p/q/r)chisq functions. Examples s <- seq(0, 3,.01) plot(s, dinvchisq(s, 3), type = 'l') f <- function(x) dinvchisq(x, 3) q <- 2
3 invexp 3 (p <- pinvchisq(q, 3)) qinvchisq(p, 3) # = q mean(rinvchisq(1e5, 3) <= q) f <- function(x) dinvchisq(x, 3, ncp = 2) q <- 1.5 (p <- pinvchisq(q, 3, ncp = 2)) qinvchisq(p, 3, ncp = 2) # = q mean(rinvchisq(1e7, 3, ncp = 2) <= q) invexp The Inverse Exponential Distribution Description Density, distribution function, quantile function and random generation for the inverse exponential distribution. Usage dinvexp(x, rate = 1, log = FALSE) pinvexp(q, rate = 1, lower.tail = TRUE, log.p = FALSE) qinvexp(p, rate = 1, lower.tail = TRUE, log.p = FALSE) rinvexp(n, rate = 1) Arguments x, q vector of quantiles. rate log, log.p lower.tail p n degrees of freedom (non-negative, but can be non-integer). logical; if TRUE, probabilities p are given as log(p). logical; if TRUE (default), probabilities are P[X <= x] otherwise, P[X > x]. vector of probabilities. number of observations. If length(n) > 1, the length is taken to be the number required.
4 4 invgamma Details The functions (d/p/q/r)invexp simply wrap those of the standard (d/p/q/r)exp R implementation, so look at, say, dexp for details. See Also dexp; these functions just wrap the (d/p/q/r)exp functions. Examples s <- seq(0, 10,.01) plot(s, dinvexp(s, 2), type = 'l') f <- function(x) dinvexp(x, 2) q <- 3 (p <- pinvexp(q, 2)) qinvexp(p, 2) # = q mean(rinvexp(1e5, 2) <= q) pinvgamma(q, 1, 2) invgamma The Inverse Gamma Distribution Description Density, distribution function, quantile function and random generation for the inverse gamma distribution. Usage dinvgamma(x, shape, rate = 1, scale = 1/rate, log = FALSE) pinvgamma(q, shape, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE) qinvgamma(p, shape, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE) rinvgamma(n, shape, rate = 1, scale = 1/rate)
5 invgamma 5 Arguments x, q vector of quantiles. shape rate scale log, log.p lower.tail p n Details inverse gamma shape parameter inverse gamma rate parameter alternative to rate; scale = 1/rate logical; if TRUE, probabilities p are given as log(p). logical; if TRUE (default), probabilities are P[X <= x] otherwise, P[X > x]. vector of probabilities. number of observations. If length(n) > 1, the length is taken to be the number required. The inverse gamma distribution with parameters shape and rate has density f(x) = rate^shape/gamma(shape) x^(-1-shape) e^(-rate/x) it is the inverse of the standard gamma parameterzation in R. The functions (d/p/q/r)invgamma simply wrap those of the standard (d/p/q/r)gamma R implementation, so look at, say, dgamma for details. See Also dgamma; these functions just wrap the (d/p/q/r)gamma functions. Examples s <- seq(0, 5,.01) plot(s, dinvgamma(s, 7, 10), type = 'l') f <- function(x) dinvgamma(x, 7, 10) q <- 2 (p <- pinvgamma(q, 7, 10)) qinvgamma(p, 7, 10) # = q mean(rinvgamma(1e5, 7, 10) <= q)
6 Index dchisq, 2 dexp, 4 dgamma, 5 dinvchisq (invchisq), 2 dinvexp (invexp), 3 dinvgamma (invgamma), 4 invchisq, 2 invexp, 3 invgamma, 4 pinvchisq (invchisq), 2 pinvexp (invexp), 3 pinvgamma (invgamma), 4 qinvchisq (invchisq), 2 qinvexp (invexp), 3 qinvgamma (invgamma), 4 rinvchisq (invchisq), 2 rinvexp (invexp), 3 rinvgamma (invgamma), 4 6
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Laboratorio di ST1 Lezione 4
Laboratorio di ST1 Lezione 4 Claudia Abundo Dipartimento di Matematica Università degli Studi Roma Tre 26 Marzo 2010 Gamma?dgamma The Gamma Distribution Description Density, distribution function, quantile
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