Calculate skewness and kurtosis based on Beta distribution in one group

This function can be used to calculate the skewness and kurtosis based on the Beta distribution. Also, this function estimate the shape parameters alpha and beta.

Usage

desbeta(
  vmean,
  vsd,
  lo,
  hi,
  method = "MM",
  rawdata = NULL,
  showFigure = FALSE,
  ...
)

Arguments

vmean: sample mean of the truncated data
vsd: sample standard deviation of the truncated data
lo: minimum possible value
hi: maximum possible value
method: when method = 'MM', the method used is the method of moments, when method = "ML', the method used to estimate the distribution is maximum likelihood
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.
...: other arguments

Value

If `showFigure = TRUE`, the output will be a list with two objects: one is the data frame of shape parameters (alpha and beta), mean and standard deviation of standard beta 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

Johnson NL, Kotz S, Balakrishnan N (1995). “Continuous univariate distributions.” In volume 289, chapter 25 Beta Distributions. John wiley & sons.

Smithson M, Verkuilen J (2006). “A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables.” Psychological methods, 11(1), 54.

Examples

data('beta_mdat')
desbeta(vmean=beta_mdat$m2[6], vsd=beta_mdat$sd2[6],
hi = beta_mdat$hi2[6], lo = beta_mdat$lo2[6], showFigure = TRUE)
#> $dat
#>      alpha      beta      mean        sd  skewness kurtosis
#> 1 3.614481 0.5718672 0.8633971 0.1508011 -1.558126 2.299977
#> 
#> $fig

#>