Calculate skewness and kurtosis based on truncated normal distribution in one group

This function can be used to calculate the skewness and kurtosis based on the truncated normal distribution. Also, it can be used to estimate the mean and variance of the parent distribution (the distribution before truncated).

Usage

destrunc(
  vmean,
  vsd,
  lo,
  hi,
  rawdata = NULL,
  showFigure = FALSE,
  xstart,
  btol,
  ftol,
  ...
)

Arguments

vmean

sample mean of the truncated data

vsd

sample standard deviation of the truncated data

lo

minimum possible value

hi

maximum possible value

rawdata

when raw data is available, we could still use it to check it figuratively, if the data was closed to the normal distribution, or truncated normal distribution.

showFigure

when showFigure = TRUE, it will display the plots with theoretical normal curve and the truncated normal curve.

xstart

see the package nleqslv

btol

see the package nleqslv

ftol

see the package nleqslv

...

other arguments

Value

If `showFigure = TRUE`, the output will be a list with two objects: one is the data frame of parent mean and standard deviation (pmean and psd), mean and standard deviation of truncated normal distribution (mean and sd), and skewness and kurtosis; the other is the theoretical figures of beta and normal distributions. If `showFigure = FALSE`, the output will be only the data frame.

References

Shah SM, Jaiswal MC (1966). “Estimation of parameters of doubly truncated normal distribution from first four sample moments.” Annals of the Institute of Statistical Mathematics, 18(1), 107--111.

Robert CP (1995). “Simulation of truncated normal variables.” Statistics and computing, 5(2), 121--125.

Barr DR, Sherrill ET (1999). “Mean and variance of truncated normal distributions.” The American Statistician, 53(4), 357--361.

See also

desbeta

Examples

data("trun_mdat")
destrunc(vmean=trun_mdat$m2[6], vsd=trun_mdat$sd2[6],
hi = 4, lo = 0, showFigure = TRUE)
#> $dat
#>      pmean       psd       tm       tsd  skewness   kurtosis
#> 1 1.505538 0.9667249 1.613387 0.8375352 0.2713042 -0.4927465
#> 
#> $fig

#> 
#example2
destrunc(vmean=trun_mdat$m1[17], vsd=trun_mdat$sd1[17],
hi = 4, lo = 0, showFigure = TRUE)
#> $dat
#>       pmean     psd      tm       tsd  skewness   kurtosis
#> 1 0.6706224 1.55863 1.44477 0.9592371 0.5321831 -0.5392483
#> 
#> $fig

#>