hmomco {lmomco}R Documentation

Hazard Functions of the Distributions

Description

This function acts as a front end to dlmomco and plmomco to compute the hazard function h(x) or conditional failure rate. The function is defined by

h(x) = frac{f(x)}{1 - F(x)}mbox{,}

where f(x) is a probability density function and F(x) is the cumulative distribution function.

To help with intuitive understanding of what h(x) means (Ugarte and others, 2008), let dx represent a small unit of measurement. Then the quantity h(x)dx can be conceptualized as the approximate probability that random variable X takes on a value in the interval [x, x+dx].

Ugarte and others (2008) continue by stating that h(x) represents the instantaneous rate of death or failure at time x, given the survival to time x has occurred. Emphasis is needed that h(x) is a rate of probability change and not a probability itself.

Usage

hlmomco(x,para)

Arguments

x A real value.
para The parameters from lmom2par or similar.

Value

Hazard rate for x.

Author(s)

W.H. Asquith

References

Ugarte, M.D., Militino, A.F., and Arnholt, A.T., 2008, Probability and statistics with R: Boca Raton, FL., CRC Press, 700 p.

See Also

plmomco, dlmomco

Examples

my.lambda <- 100
para <- vec2par(c(0,my.lambda), type="exp")

x <- seq(40:60)
hlmomco(x,para) # returns vector of 0.01 
# because the exponential distribution has a constant 
# failure rate equal to 1/scale or 1/100 as in this example.

[Package lmomco version 0.96.3 Index]