Analyzing the Best Fitted Probabilistic Model for the Seasonal Rainfall Data in Khulna Region of Bangladesh

There are several pieces of research on the statistical modeling of rainfall data in Bangladesh. Since all the seasons of a year do not receive a similar amount of rainfall, hence one single statistical model might not be able to explain the pattern of rainfall at any season of a year. According to the climatologists, Bangladesh has four seasons which are Monsoon, Post-monsoon, Summer, and Winter based on the geographical characteristics of this country. This paper aims to determine the best-fitted probability distribution model for the monthly rainfall data of each particular season in the Khulna district of Bangladesh using the rainfall data of the Khulna region from 1951 to 2018. Very commonly used seven continuous distributions- Normal, Weibull, Gamma, Log-normal, Exponential, Cauchy, and Logistic distributions were used to model the data and to evaluate the performances of the distributions, three non-parametric goodness-of-fit tests were conducted, and AIC, BIC values were calculated. Parameters of the distributions were estimated by the maximum likelihood method. The best-fit result of each season was taken as the distribution with the lowest AIC and BIC values. Among the seven distributions, the Gamma distribution showed the best-fit results of the monthly rainfall data for the Monsoon, Post-Monsoon, and Winter Season, and the Weibull distribution showed the best-fit result for Summer Season.

Some Resultats on Optimal Allocation of Policy Limits and Deductibles: Mixture Model

The main purpose of this paper is to introduce and investigate stochastic orders of scalar products of random vectors. We study the problem of finding maximal expected utility for some functional on insurance portfolios involving some additional (independent) randomization. Furthermore, applications in policy limits and deductible are obtained, we consider the scalar product of two random vectors which separates the severity effect and the frequency effect in the study of the optimal allocation of policy limits and deductibles. In that respect, we obtain the ordering of the optimal allocation of policy limits and deductibles when the dependence structure of the losses is unknown. Our application is a further study of [1 − 6].

Mixingale Estimation Function for SPDEs with Random Sampling

We study the mixingale estimation function estimator of the drift parameter in the stochastic partial differential equation when the process is observed at the arrival times of a Poisson process. We use a two stage estimation procedure. We first estimate the intensity of the Poisson process. Then we substitute this estimate in the estimation function to estimate the drift parameter. We obtain the strong consistency and the asymptotic normality of the mixingale estimation function estimator.

A Novel Chen Extension: Theory, Characterizations and Different Estimation Methods

In this work, we derive a novel extension of Chen distribution. Some statistical properties of the new model are derived. Numerical analysis for mean, variance, skewness and kurtosis is presented. Some characterizations of the proposed distribution are presented. Different classical estimation methods under uncensored schemes such as the maximum likelihood, Anderson-Darling, weighted least squares and right-tail Anderson–Darling methods are considered. Simulation studies are performed in order to compare and assess the above-mentioned estimation methods. For comparing the applicability of the four classical methods, two application to real data set are analyzed.

On the T-X Class of Topp Leone-G Family of Distributions: Statistical Properties and Applications

This article investigates the T-X class of Topp Leone- G family of distributions. Some members of the new family are discussed. The exponential-Topp Leone-exponential distribution (ETLED) which is one of the members of the family is derived and some of its properties which include central and non-central moments, quantiles, incomplete moments, conditional moments, mean deviation, Bonferroni and Lorenz curves, survival and hazard functions, moment generating function, characteristic function and R`enyi entropy are established. The probability density function (pdf) of order statistics of the model is obtained and the parameter estimation is addressed with the maximum likelihood method (MLE). Three real data sets are used to demonstrate its application and the results are compared with two other models in the literature.