Mixture of two exponential distributions

Description

Probability functions associated to the mixture of two exponential distributions.

Usage

   dmixexp2(x, prob1,
            rate1 = 1.0, rate2 = rate1 + delta, delta,
            log = FALSE)
   pmixexp2(q, prob1,
            rate1 = 1.0, rate2 = rate1 + delta, delta,
            log = FALSE)
   qmixexp2(p, prob1,
            rate1 = 1.0, rate2 = rate1 + delta, delta)
   rmixexp2(n, prob1,
            rate1 = 1.0, rate2 = rate1 + delta, delta)
   hmixexp2(x, prob1,
            rate1 = 1.0, rate2 = rate1 + delta, delta)
   Hmixexp2(x, prob1,
            rate1 = 1.0, rate2 = rate1 + delta, delta)

Arguments

Details

The density function is the mixture of two exponential densities

f(x) = α_1 λ_1 exp(- λ_1 x) + (1 - α_1) λ_2 exp(- λ_2 x) (x > 0)

where α_1 is the probability given in prob1 while λ_1 andλ_2 are the two rates given in rate1 and rate2.

A 'naive' identifiability constraint is

λ_1 < λ_2

i.e. rate1 < rate2, corresponding to the simple constraint delta > 0. The parameter delta can be given instead of rate2.

The mixture distribution has a decreasing hazard, increasing Mean Residual Life (MRL) and has a thicker tail than the usual exponential. However the hazard, MRL have a finite non zero limit and the distribution behaves as an exponential for large return levels/periods.

The quantile function is not available in closed form and is computed using a dedicated numerical method.

Value

dmiwexp2, pmiwexp2, qmiwexp2, evaluates the density, the distribution and the quantile functions. dmixexp2 generates a vector of n random draws from the distribution. hmixep2 gives hazard rate and Hmixexp2 gives cumulative hazard.

Examples

rate1 <- 1.0
rate2 <- 4.0
prob1 <- 0.8
qs <- qmixexp2(p = c(0.99, 0.999), prob1 = prob1,
               rate1 = rate1, rate2 = rate2) 
x <- seq(from = 0, to = qs[2], length.out = 200)
F <- pmixexp2(x, prob1 = prob1, rate1 = rate1, rate2 = rate2)
plot(x, F, type = "l", col = "orangered", lwd = 2,
     main = "Mixexp2 distribution and quantile for p = 0.99")
abline(v = qs[1])
abline(h = 0.99)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(Renext)
Loading required package: evd
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/Renext/MixExp2.Rd_%03d_medium.png", width=480, height=480)
> ### Name: MixExp2
> ### Title: Mixture of two exponential distributions
> ### Aliases: MixExp2 dmixexp2 rmixexp2 pmixexp2 qmixexp2 hmixexp2 Hmixexp2
> ### Keywords: distribution
> 
> ### ** Examples
> 
> rate1 <- 1.0
> rate2 <- 4.0
> prob1 <- 0.8
> qs <- qmixexp2(p = c(0.99, 0.999), prob1 = prob1,
+                rate1 = rate1, rate2 = rate2) 
> x <- seq(from = 0, to = qs[2], length.out = 200)
> F <- pmixexp2(x, prob1 = prob1, rate1 = rate1, rate2 = rate2)
> plot(x, F, type = "l", col = "orangered", lwd = 2,
+      main = "Mixexp2 distribution and quantile for p = 0.99")
> abline(v = qs[1])
> abline(h = 0.99)
> 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>