Distribution Functions for a Mixture Distribution

pdf, cdf, inverse cdf, and random deviates of a user defined mixture distribution with equal weights.

.checkFunctions(functionList)

qMixtureDistribution(p, functionList, xMin, xMax, nPoints = 1000,
  logScale = FALSE)

rMixtureDistribution(n, functionList)

pMixtureDistribution(x, functionList)

dMixtureDistribution(x, functionList)

Arguments

functionList

A list of functions forming the mixture distribution. The functions must be a continuous CDF dependent on 'x'.
p

A vector of probabilities.
xMin

The minimum value for which probabilities and quantiles are calculated.
xMax

The maximum value for which probabilities and quantiles are calculated.
nPoints

The number of points at which the mixed CDF is calculated. Default=1000.
logScale

Are the CDF estimates to be performed on a logarithmic scale? Default=FALSE
n

The number of random deviates to compute
x

The value at which the cdf or pdf are computed

Value

A vector of densities, probabilities, quantiles, or random deviates from the mixture distribution.

Examples

  qMixtureDistribution(c(0.5), list("pnorm(x, 1, 0.1)","pnorm(x, 2, 0.1)",
                                    "pnorm(x, 3, 0.1)"), 0, 4)
#> [1] 2
  pMixtureDistribution(2, list("pnorm(x, 1, 0.1)","pnorm(x, 2, 0.1)",
                               "pnorm(x, 3, 0.1)"))
#> [1] 0.5
  pMixtureDistribution(c(0.5,1,2,4,5,6),
                       list("pnorm(x, 1, 0.1)","pnorm(x, 2, 0.1)",
                            "pnorm(x, 3, 0.1)"))
#> [1] 9.555052e-08 1.666667e-01 5.000000e-01 1.000000e+00 1.000000e+00
#> [6] 1.000000e+00
  x1 <- rMixtureDistribution(10000, list("pnorm(x, 1, 0.1)",
                                         "pnorm(x, 2, 0.1)",
                                         "pnorm(x, 3, 0.1)"))
  mean(x1)
#> [1] 1.999914
  rMixtureDistribution(1, list("pnorm(x, 1, 0.1)","pnorm(x, 2, 0.1)",
                               "pnorm(x, 3, 0.1)"))
#> Warning: There are not enough requested samples to sample once from each function
#> rnorm(n, 1, 0.1) 
#>         0.796579 
  rMixtureDistribution(3, list("pnorm(x, 1, 0.1)","pnorm(x, 2, 0.1)",
                               "pnorm(x, 3, 0.1)"))
#> rnorm(n, 1, 0.1) rnorm(n, 2, 0.1) rnorm(n, 3, 0.1) 
#>         1.172192         2.138209         2.924062 
  rMixtureDistribution(4, list("pnorm(x, 1, 0.1)","pnorm(x, 2, 0.1)",
                               "pnorm(x, 3, 0.1)"))
#> [1] 1.056129 1.088525 1.968245 2.038495
  integrate(dMixtureDistribution, 0, 4,
            functionList = list("pnorm(x, 1, 0.1)","pnorm(x, 2, 0.1)",
                                "pnorm(x, 3, 0.1)"))
#> 1 with absolute error < 8.2e-05
  integrate(dMixtureDistribution, 0, Inf,
            functionList = list("pnorm(x, 1, 0.1)","plnorm(x, .2, 0.1)",
                                "pnorm(x, 3, 0.1)"))
#> 1 with absolute error < 7e-05