fit.dist {gnlm}

Fit Probability Distributions to Frequency Data

Description

fit.dist fits the distributions in Chapter 4 of Lindsey (1995, 2003 2nd edn): binomial, beta-binomial, Poisson, negative binomial, geometric, zeta, normal, log normal, inverse Gauss, logistic, Laplace, Cauchy, Student t, exponential, Pareto, gamma, and Weibull to frequency (histogram) data, possibly plotting the frequency polygon of fitted values with the histogram.

Usage

fit.dist(y, ni, distribution = "normal", breaks = FALSE, delta = 1,
  censor = FALSE, exact = TRUE, plot = FALSE, add = FALSE,
  xlab = deparse(substitute(y)), ylab = "Probability",
  xlim = range(y), main = paste("Histogram of",
  deparse(substitute(y))), ...)

Arguments

y

Vector of observations.

ni

Corresponding vector of frequencies.

distribution

Character string specifying the distribution.

breaks

If TRUE, y contains breaks between categories instead of mid-points.

delta

Scalar or vector giving the unit of measurement (always one for discrete data) for each response value, set to unity by default. For example, if a response is measured to two decimals, delta=0.01.

censor

If TRUE, the last category is right censored.

exact

If FALSE, uses the approximations for certain distributions in Lindsey (1995).

plot

If TRUE, plots the histogram of observed frequencies and the frequency polygon of fitted values.

add

If TRUE, adds a new frequency polygon of fitted values without replotting the histogram.

xlab

Plotting control options.

ylab

Plotting control options.

xlim

Plotting control options.

main

Plotting control options.

...

Plotting control options.

Author(s)

J.K. Lindsey

References

Lindsey, J.K. (1995) Introductory Statistics: A Modelling Approach. Oxford: Oxford University Press.

Examples

f <- c(215, 1485, 5331, 10649, 14959, 11929, 6678, 2092, 342)
y <- seq(0,8)
fit.dist(y, f, "binomial", plot=TRUE, xlab="Number of males",
	main="Distribution of males in families of 8 children")
#
f <- c(1,1,6,3,4,3,9,6,5,16,4,11,6,11,3,4,5,6,4,4,5,1,1,4,1,2,
	0,2,0,0,1)
y <- seq(1100,4100,by=100)
fit.dist(y, f, "normal", delta=100, plot=TRUE,
	xlab="Monthly salary (dollars)",
	main="Distribution of women mathematicians' salaries")
fit.dist(y, f, "log normal", delta=100, plot=TRUE, add=TRUE, lty=3)
fit.dist(y, f, "logistic", delta=100, exact=FALSE, plot=TRUE, add=TRUE, lty=2)