Bayesian Approaches for Poisson Distribution Parameter Estimation

The Bayesian approach, a non-classical estimation technique, is very widely used in statistical inference for real world situations. The parameter is considered to be a random variable, and knowledge of the prior distribution is used to update the parameter estimation. Herein, two Bayesian approaches for Poisson parameter estimation by deriving the posterior distribution under the squared error loss or quadratic loss functions are proposed. Their performances were compared with frequentist (maximum likelihood estimator) and Empirical Bayes approaches through Monte Carlo simulations. The mean square error was used as the test criterion for comparing the methods for point estimation; the smallest value indicates the best performing method with the estimated parameter value closest to the true parameter value. Coverage Probabilities (CPs) and average lengths (ALs) were obtained to evaluate the performances of the methods for constructing confidence intervals. The results reveal that the Bayesian approaches were excellent for point estimation when the true parameter value was small (0.5, 1 and 2). In the credible interval comparison, these methods obtained CP values close to the nominal 0.95 confidence level and the smallest ALs for large sample sizes (50 and 100), when the true parameter value was small (0.5, 1 and 2). Doi: 10.28991/esj-2021-01310 Full Text: PDF

Estimating the potential of wind energy resources using Weibull parameters: A case study of the coastline region of Dar es Salaam, Tanzania

This study aimed to compare the graphical method (GM) and standard deviation method (SDM), based on analyses and efficient Weibull parameters by estimating future wind energy potential in the coastline region of Dar es Salaam, Tanzania. Hence, the conclusion from the numerical method comparisons will also determine suitable wind turbines that are cost-effective for the study location. The wind speed data for this study were collected by the Tanzania Meteorological Authority Dar es Salaam station over the period of 2017 to 2019. The two numerical methods introduced in this study were both found to be appropriate for Weibull distribution parameter estimation in the study area. However, the SDM gave a higher value of the Weibull parameter estimation than the GM. Furthermore, the five selected commercial wind turbine models that were simulated in terms of performance were based on a capacity factor using the SDM and were both over 25% the recommended capacity factor value. The Polaris P50-500 commercial wind turbine is recommend as a suitable wind turbine to be installed in the study area due to its maximum annual capacity factor value over 3 years.

Pricing of Premium for Automobile Insurance using Bayesian Method

The aggregate claim model can be used to determine the amount of premium charged to the insured by the insurance company. This model consists of two mutually independent random variables, namely the number of claims that occur per period and the amount of claim for each event. In this study, the number of claims is Poisson distributed, and the amount of claim is distributed by generalized extreme value (GEV). The Bayes method is used to estimate the parameters of each distribution. Parameter estimation results are used to calculate the expectations and variances of the aggregate claim model which are then used to calculate insurance premiums. Based on the estimation results, the amount of premium charged to the insured ranges from IDR 3,831,480 to IDR 6,443,860.