# BMS

0th

Percentile

##### Beta Shape-Parameter Given Location-Parameters, Mean, Variance, Skewness, Kurtosis and Alpha Shape-Parameter of a Four-Parameter Beta PDD.

Calculates the Beta value required to produce a Beta probability density distribution with defined moments and parameters. Be advised that not all combinations of moments and parameters can be satisfied (e.g., specifying mean, variance, skewness and kurtosis uniquely determines both location-parameters, meaning that the value of the lower-location parameter will take on which ever value it must, and cannot be specified).

##### Usage
BMS(
mean = NULL,
variance = NULL,
skewness = NULL,
kurtosis = NULL,
l = 0,
u = 1,
alpha = NULL,
sd = NULL
)
##### Arguments
mean

The mean (first raw moment) of the target Standard Beta probability density distribution.

variance

The variance (second central moment) of the target Standard Beta probability density distribution.

skewness

The skewness (third standardized moment) of the target Beta probability density distribution.

kurtosis

The kurtosis (fourth standardized moment) of the target Beta probability density distribution.

l

The lower-bound of the Beta distribution. Default is 0 (i.e., the lower-bound of the Standard, two-parameter Beta distribution).

u

The upper-bound of the Beta distribution. Default is 1 (i.e., the upper-bound of the Standard, two-parameter Beta distribution).

alpha

Optional specification of the Alpha shape-parameter of the target Beta distribution. Finds then the Beta parameter necessary to produce a distribution with the specified mean, given specified Alpha, l, and u parameters.

sd

Optional alternative to specifying var. The standard deviation of the target Standard Beta probability density distribution.

##### Value

A numeric value representing the required value for the Beta shape-parameter in order to produce a Standard Beta probability density distribution with the target mean and variance, given specified lower- and upper bounds of the Beta distribution.

• BMS
##### Examples
# NOT RUN {
# Generate some fictional data. Say, 100 individuals take a test with a
# maximum score of 100 and a minimum score of 0, rescaled to proportion
# of maximum.
set.seed(1234)
testdata <- rbinom(100, 100, rBeta.4P(100, .25, .75, 5, 3)) / 100
hist(testdata, xlim = c(0, 1))

# To find the beta shape-parameter of a Standard (two-parameter) Beta
# distribution with the same mean and variance as the observed-score
# distribution using BMS():
BMS(mean(testdata), var(testdata))

# To find the beta shape-parameter of a four-parameter Beta
# distribution with specified lower- and upper-bounds of l = 0.25 and
# u = 0.75 using BMS:
BMS(mean(testdata), var(testdata), .25, .75)
# }

Documentation reproduced from package betafunctions, version 1.4.0, License: CC0

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