Beta Distribution: Basics
What is beta Distribution?
Looking for Beta distribution assignment help? You are at Right Place.As one of the quantitative tools categorized under Probability Theory and Statistics, the beta distribution is a continuous probability distribution function defined between the intervals (0,1). In this distribution, there are two positively shaped parameters. Each of the two terms are denoted by alpha (α) and beta (β). They are characterized as exponentials of the random variable and hence determine the shape of the probability distribution. This tool is used to measure the probability of success in an experiment.
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The above figure shows a beta distribution for different levels of (α) given that β=8.
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How to statistically understand a Beta Distribution?
Let us assume, the probability of success in an experiment is ‘x.’ Hence the possibility of failure is ‘1-x’. The two terms can take any value between 0 and 1. We assume that there is uniform chance that it could be any variable between 0 and 1. This is a uniform distribution between the range 0 and 1(denoted by U[0,1]). If the experiment is conducted ‘n’ times with ‘k’ being the number of times the experiment was a success. The experiment would be a failure ‘n-k’ times. Based on these outcomes, we redistribute the uniform experiment based on the observed outcome. This conditional distribution of x based on the ‘k’ and ‘n-k’ is known as Beta Distribution.’ For practical problems, access the beta distribution homework help section.
What are the Characteristics of Beta Distribution?
The Beta function has certain characteristics. These characteristics define some ground rules for the efficient use and functioning of Beta function and the Beta Distribution
- The Beta Function of the two terms alpha and beta is symmetric
- The two terms α and beta β are greater than 0 and less than infinity (∞)
- The beta function can be expressed in terms of gamma function
What is an Incomplete Beta Function?
In the case of an incomplete Beta Function, the integral which defines the beta function is generalized. Let us say, the interval of integration is changed to ‘x.’ The range of the beta function will be between (0,X’) instead of (0,1). The incomplete Beta function can be expressed as follows
The incomplete beta function is computed by the use of specialized computer algorithms.
What are the applications of Beta Distribution?
The Beta Distribution has a variety of applications. Some of the important applications of beta distribution are
- The ‘rule of succession’ is the perfect example of the application of a Beta Distribution. The beta distribution allows effective modeling of random probabilities. It can be a substantial tool particularly in the context of Bayesian Analysis
- It plays an important part in the theory of order statistics. With the use of the beta distribution and theory of probability integral transform, it is possible to derive any individual order statistic from a continuous distribution
- The beta distribution is also useful in task duration modeling. This allows estimation of time taken to complete a task and the cost associated with the task. It is a crucial component in modern day project management. It is wide used by many corporates to efficiently carry out their daily operations.
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