hmomco {lmomco} | R Documentation |
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.
hlmomco(x,para)
x |
A real value. |
para |
The parameters from lmom2par or similar. |
Hazard rate for x
.
W.H. Asquith
Ugarte, M.D., Militino, A.F., and Arnholt, A.T., 2008, Probability and statistics with R: Boca Raton, FL., CRC Press, 700 p.
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.