betamoments {betafunctions}

Compute Moments of Two-to-Four Parameter Beta Probability Density Distributions.

Description

Computes Raw, Central, or Standardized moment properties of defined Beta probability density distributions.

Usage

betamoments(
  alpha,
  beta,
  l = 0,
  u = 1,
  types = c("raw", "central", "standardized"),
  orders = 4
)

Arguments

alpha

The alpha shape parameter.

beta

The beta shape parameter.

l

The first (lower) location parameter.

u

The second (upper) location parameter.

types

A character vector determining which moment-types are to be calculated. Permissible values are "raw", "central", and "standardized".

orders

The number of moment-orders to be calculated for each of the moment-types.

Value

A list of moment types, each a list of moment orders.

References

Hanson, B. A (1991). Method of Moments Estimates for the Four-Parameter Beta Compound Binomial Model and the Calculation of Classification Consistency Indexes. American College Testing Research Report Series.

Examples

# Assume some variable follows a four-parameter Beta distribution with
# location parameters l = 0.25 and u = 0.75, and shape parameters alpha = 5
# and beta = 3. To compute the first four raw, central, and standardized
# moments of this distribution using betamoments():
betamoments(alpha = 5, beta = 3, l = 0.25, u = 0.75,
types = c("raw", "central", "standardized"), orders = 4)