cdftexp: Cumulative Distribution Function of the Truncated Exponential Distribution

Description

This function computes the cumulative probability or nonexceedance probability of the Truncated Exponential distribution given parameters ($\xi$ and $\alpha$) of the distribution computed by partexp. The cumulative distribution function of the distribution is

$F (x) = \frac{1 - \exp (- t / α)}{1 - \exp (- ξ / α)},$

where $F(x)$ is the nonexceedance probability for the quantile $x$, $\xi$ is a location parameter, $\alpha$ is a scale parameter, and $0 \le x \le \xi$. The distribution has $0 < \tau_2 <= 1="" 2$,="" $\xi=""> 0$, and $1/\alpha \ne 0$.

Usage

cdftexp(x, para)

Arguments

A real value.

para

The parameters from partexp or similar.

Value

Nonexceedance probability ($F$) for $x$.

References

Vogel, R.M., Hosking, J.R.M., Elphick, C.S., Roberts, D.L., and Reed, J.M., 2008, Goodness of fit of probability distributions for sightings as species approach extinction: Bulletin of Mathematial Biology, v. 71, no. 3, pp. 701--719.

Examples

Run this code

lmr <- vec2lmom(c(40,0.38), lscale=FALSE)
  cdftexp(50,partexp(lmr))

  # Vogel and others (2008) example sighting times for the bird
  # Eskimo Curlew, inspection shows that these are fairly uniform.
  # There is a sighting about every year to two.
  T <- c(1946, 1947, 1948, 1950, 1955, 1956, 1959, 1960, 1961,
         1962, 1963, 1964, 1968, 1970, 1972, 1973, 1974, 1976,
         1977, 1980, 1981, 1982, 1982, 1983, 1985)
  R <- 1945 # beginning of record
  S <- T - R
  PARcurlew <- partexp(lmoms(S))
  Xmax <- quatexp(1, PARcurlew)
  X <- seq(0,Xmax, by=1)
  plot(X, cdftexp(X,PARcurlew), type="l")

  # Plot looks not curved enough to show the texp?
  # Try S <- S^2 and rerunning the last four lines.

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