GammaDist {IPMbook}

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))