Beta distributions: A computer program for probabilities and fractile points (original) (raw)
Related papers
On some Applications of Beta Function in some Statistical Distributions
Researcher, 2015
The study established some applications of beta function in probability and cumulative density functions. Just as the gamma function for integers describe factorials, the beta function also defines a binomial coefficient after adjusting indices. The incomplete beta function is a generalization of the beta function that replaces the definite integral of the beta function with an independent integral. In the study, the graph of beta distribution using MATLAB is shown. Further, the study showed how beta and gamma are related theoretically
Simplified use of the beta distribution and sensitivity to the bound locations
Structural Safety, 1985
The parameters used in the reliability analysis of soil and structural systems are generally bounded and skewed random quantities. This is the case not only for variables representing the strength of materials and the intensity of loads, but also for the functions used as safety indexes, like the so-called "factor of safety".
Beta PDF, numerical computation
2015
The computation of the Beta PDF is discussed and algorithms are described which permit calculation of the PDF over the full range of its parameters without recourse to approximations or polynomial expansions. This is achieved by giving simple rules for the treatment of the trivial cases and a new algorithm for the general cases, particularly for the cases where the PDF becomes infinity at the extremes of the range. The problems of underflow and overflow when performing the calculations on a digital computer are also addressed, and a general prescaling procedure is presented which overcomes these problems. It is shown that the new algorithms perform more efficiently than commercial mathematical packages.
Sankhya B, 2014
A new family of skewed distributions referred to as modified beta distributions is presented. Some properties of the new family including estimation procedures are derived. A real data application as well as simulation studies are described to show superior performance versus known models.
2009
For the first time, we introduce the so-called beta alpha distribution which generalizes the alpha distribution (Katsav (1968), Wager and Barash (1971)). Expansions for the cumulative distribution and density functions that do not involve complicated functions are derived. We obtain expressions for its moments and for the moments of order statistics. The estimation of parameters is approached by the method of maximum likelihood and the expected information matrix is derived. The usefulness of the beta alpha distribution is illustrated in an analysis of a real data set. The new model is quite flexible in analyzing positive data and it is an important alternative to the gamma, Weibull, generalized exponential, beta exponential and Birnbaum-Saunders distributions.
Some Mathematical Characteristics of the Beta Density Function of Two Variables
emis.ams.org
Some well known results on the bivariate beta distribution have been reviewed. Corrected product moments are derived. These moments will be important for studying further characteristics of the distribution. The distribution of the ratio of two correlated beta variables has been derived and used to obtain a new reliability expression. Other interesting distributions stemming from the correlated beta variables are also derived.
Accurate Numerical Computation of the Beta PDF
The computation of the Beta PDF is discussed and algorithms are described which permit calculation of the PDF over the full range of its parameters without recourse to approximations or polynomial expansions. This is achieved by giving simple rules for the treatment of the trivial cases and a new algorithm for the general cases, particularly for the cases where the PDF becomes infinity at the extremes of the range. The problems of underflow and overflow when performing the calculations on a digital computer are also addressed, and a general prescaling procedure is presented which overcomes these problems. It is shown that the new algorithms perform more efficiently than commercial mathematical packages.
A New 3-Parameter Bounded Beta Distribution: Properties, Estimation, and Applications
Axioms
This study presents a new three-parameter beta distribution defined on the unit interval, which can have increasing, decreasing, left-skewed, right-skewed, approximately symmetric, bathtub, and upside-down bathtub shaped densities, and increasing, U, and bathtub shaped hazard rates. This model can define well-known distributions with various parameters and supports, such as Kumaraswamy, beta exponential, exponential, exponentiated exponential, uniform, the generalized beta of the first kind, and beta power distributions. We present a comprehensive account of the mathematical features of the new model. Maximum likelihood methods and a Bayesian method under squared error and linear exponential loss functions are presented; also, approximate confidence intervals are obtained. We present a simulation study to compare all the results. Two real-world data sets are analyzed to demonstrate the utility and adaptability of the proposed model.