pBetaMS {betafunctions}

Probability of Some Specific Observation under the Beta Probability Density Distribution with Specific Location Parameters, Mean, and Variance.

Description

Calculates the probability of some specific observation falling under a specified interval ([0, x] or [x, 1]) under the Standard Beta probability density distribution with defined mean and variance or standard deviation.

Usage

pBetaMS(q, mean, variance = NULL, sd = NULL, lower.tail = TRUE, l = 0, u = 1)

Arguments

q

A specific point on the x-axis of the Standard Beta probability density distribution with a defined mean and variance.

mean

The mean of the target Standard Beta probability density distribution.

variance

The variance of the target Standard Beta probability density distribution.

sd

The standard deviation of the target Standard Beta probability density distribution.

lower.tail

Whether the density that should be considered is between the lower-end (i.e., [0 -> x]) or the higher-end of the distribution (i.e., [x -> 1]).

l

The lower-bound location parameter. Default set to 0 (the standard Beta distribution).

u

The upper-bound location parameter. Default set to 1 (the standard Beta distribution).

Value

A value representing the probability of a random draw from the Standard Beta probability density distribution with a defined mean and variance being from one of two defined intervals (i.e., [0 -> x] or [x -> 1]).

Examples

# To compute the proportion of the density under the lower-end tail of a
# point along the Standard (two-parameter) Probability Density Distribution
# (e.g., 0.5) with mean of 0.6 and variance of 0.04:
pBetaMS(q = 0.5, mean = 0.6, variance = 0.04)

# To compute the proportion of the density under the lower-end tail of a
# point along the Four-Parameter Beta Probability Density Distribution
# (e.g., 50) with mean of 60 and variance of 400, and lower-bound of 0 and
# upper-bound of 100:
pBetaMS(q = 50, mean = 60, variance = 400, l = 0, u = 100)