GammaDist: The gamma distribution

In IPMbook: Functions and Data for the Book 'Integrated Population Models'

The gamma distribution

Description

Density, distribution function, quantile function and random number generation for the gamma distribution with parameters mean and sd. These are wrappers for stats::dgamma, etc. getGammaPar returns the shape and rate parameters.

Usage

dgamma2(x, mean, sd)
pgamma2(q, mean, sd, lower.tail=TRUE, log.p=FALSE)
qgamma2(p, mean, sd, lower.tail=TRUE, log.p=FALSE)
rgamma2(n, mean, sd)
getGammaPar(mean, sd)

Arguments

x	vector of parameter values.
q	vector of quantiles.
p	vector of probabilities.
n	number of random draws required.
mean	mean of the gamma distribution.
sd	standard deviation of the gamma distribution.
lower.tail	logical; if TRUE (default), cumulative probabilities up to x, otherwise, above x.
log.p	logical; if TRUE, probabilities p are given as log(p).

Value

dgamma2 gives the density, pgamma2 gives the distribution function, qgamma2 gives the quantile function, and rgamma2 generates random deviates.

getGammaPar returns a 2-column matrix with the shape and rate parameters corresponding to mean and sd.

Author(s)

Mike Meredith

See Also

See the stats functions dgamma, pgamma, qgamma, rgamma.

Examples

# Plot some curves with dgamma2
xx <- seq(0, 20, length.out=101)
plot(xx, dgamma2(xx, 5, 1), xlab="x", ylab="Probability density",
  main="Gamma curves with mean = 5", type='l', lwd=2)
lines(xx, dgamma2(xx, 5, 2), col='darkgreen', lwd=2)
lines(xx, dgamma2(xx, 5, 4), col='red', lwd=2)
lines(xx, dgamma2(xx, 5, 8), col='blue', lwd=2)
abline(v=5, lty=3, lwd=2)
legend('topright', paste("sd =", c(1,2,4,8)), lwd=2,
  col=c('black', 'darkgreen', 'red', 'blue'), bty='n')

# Cumulative plots with pgamma2
plot(xx, pgamma2(xx, 5, 1), xlab="x", ylab="Cumulative probability",
  main="Gamma curves with mean = 5", type='l', lwd=2)
lines(xx, pgamma2(xx, 5, 2), col='darkgreen', lwd=2)
lines(xx, pgamma2(xx, 5, 4), col='red', lwd=2)
lines(xx, pgamma2(xx, 5, 8), col='blue', lwd=2)
abline(v=5, lty=3, lwd=2)
legend('bottomright', paste("sd =", c(1,2,4,8)), lwd=2,
  col=c('black', 'darkgreen', 'red', 'blue'), bty='n')

# Generate random draws and plot a histogram
rnd <- rgamma2(1e5, 5, 2)
hist(rnd, freq=FALSE)
# Add the curve:
lines(xx, dgamma2(xx, 5, 2), col='darkgreen', lwd=2)

# Get shape and rate parameters for mean = 5 and sd = c(1,2,4,8)
getGammaPar(mean = 5, sd = c(1,2,4,8))

IPMbook documentation built on Aug. 22, 2023, 1:07 a.m.