The BETA.DIST function in Google Sheets is used to calculate the cumulative distribution function or probability density function of a beta distribution, commonly used in statistics for modeling random variables. This function is essential for analyzing probabilities and making informed decisions in various fields such as finance, engineering, and social sciences.

Syntax

BETA.DIST(x, alpha, beta, cumulative, [A], [B])

• x: The value at which you want to evaluate the function.
• alpha: The parameter that determines the shape of the distribution.
• beta: The second shape parameter that works with alpha.
• cumulative: A boolean value where TRUE returns the cumulative probability function and FALSE returns the probability density function.
• [A]: (Optional) The lower bound of the distribution.
• [B]: (Optional) The upper bound of the distribution.

Example #1

=BETA.DIST(0.5, 2, 3, TRUE)

This function calculates the cumulative probability for a beta distribution where the parameters are set to alpha = 2 and beta = 3. The result could be 0.6875, indicating that there’s a 68.75% chance a random variable will be less than or equal to 0.5 under this distribution.

Example #2

=BETA.DIST(0.5, 2, 3, FALSE)

Here, the function evaluates the probability density function at x = 0.5 with the same shape parameters as above. The result might be 0.5625, which shows the relative likelihood of the variable being exactly 0.5.

Example #3

=BETA.DIST(0.5, 2, 3, TRUE, 0, 1)

This version establishes the lower and upper bounds of the distribution as 0 and 1, returning a cumulative probability of 0.6875 for x = 0.5, effectively tailoring the beta distribution to this specified range.

Error handling

• NUM!: Occurs if the value of x is outside the bounds defined by A and B. This indicates that the input is invalid.
• VALUE!: This error appears if any of the parameters are not numbers or if the cumulative argument is not TRUE or FALSE.
• DIV/0!: This happens when both alpha and beta are less than or equal to 0, indicating undefined behavior in the beta distribution.

Conclusion

In summary, the BETA.DIST function in Google Sheets is a versatile tool for statistical analysis involving beta distributions. By computing probabilities and densities based on shape parameters, users can effectively model scenarios involving random variables, making informed predictions in various applications across disciplines.