The objective of this methodological-academic chapter is to
provide a detailed introduction to the Beta distribution, with examples applied
to the social and health sciences using data randomly generated from Beta
distributions. This continuous distribution maintains its status as a
well-recognized statistical tool in mathematical statistics but practitioners
in these fields rarely apply it despite its wide modeling capabilities for
probabilities, proportions and bounded data. The chapter begins with a
historical overview to provide context, followed by an explanation of its
support, parameters, and key functions, including density, cumulative
distribution, quantile, moment-generating, and characteristic functions.
Descriptive measures such as central tendency, variation, and shape are also
discussed. The chapter then covers parameter estimation, focusing on the method
of moments and maximum likelihood. The fit of a random sample to a Beta
distribution with unknown parameters is tested using the G test and
quantile-quantile plot. Additionally, the chapter presents the associated
limiting distributions and generalizations. Four examples illustrate
applications of the Beta distribution. The first example shows how to compute
probabilities and descriptive measures when the two parameters of the
distribution are known. The second example estimates the two shape parameters
(alpha and beta) using the method of moments, calculates descriptive measures
and performs probability calculations. The third example estimates alpha and
beta, along with their standard errors and confidence intervals, using
likelihood methods. The fourth example tests the goodness of fit of a sample to
a Beta distribution using the G-test and the QQ plot. The work provides
accessibility by including appendices containing R scripts for all calculations
so researchers with different statistical abilities can benefit from this
resource. The text closes with conclusions and suggestions for using the Beta
distribution. This chapter connects mathematical theory to practical examples
along with computational tools to simplify the understanding of Beta
distribution thereby advancing its adoption across social and health science
data modeling and analysis. Researchers can now exploit this flexible
distribution across policy evaluation, clinical trials and behavioral studies
to enhance their data-driven decision-making capacity.
Author
(s) Details
José
Moral de la Rubia
School of Psychology, Universidad Autónoma de Nuevo León, Street.
Dr. Carlos Canseco 110. Col. Mitras Centro, C.P. 64460. Monterrey, Nuevo León,
México.
Please see the book here:- https://doi.org/10.9734/bpi/mcsru/v3/4354
