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Research Article Open access CC BY 4.0

Probability Density Functions for Prediction Using Normal and Exponential Distribution

Kunio Takezawa

Journal of Advances in Mathematics and Computer Science · pp. 40–52 · Published 19 Dec 2021

10.9734/jamcs/2021/v36i1030410

Abstract

When data are found to be realizations of a specific distribution, constructing the probability density function based on this distribution may not lead to the best prediction result. In this study, numerical simulations are conducted using data that follow a normal distribution, and we examine whether probability density functions that have shapes different from that of the normal distribution can yield larger log-likelihoods than the normal distribution in the light of future data. The results indicate that fitting realizations of the normal distribution to a different probability density function produces better results from the perspective of predictive ability. Similarly, a set of simulations using the exponential distribution shows that better predictions are obtained when the corresponding realizations are fitted to a probability density function that is slightly different from the exponential distribution. These observations demonstrate that when the form of the probability density function that generates the data is known, the use of another form of the probability density function may achieve more desirable results from the standpoint of prediction.

Exponential distribution future data log-likelihood normal distribution predictive estimator probability density function

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