##### A Short Study on Bias Present in Classical Random Processes

Ayush Verma

Asian Journal of Probability and Statistics, Page 30-34
DOI: 10.9734/ajpas/2021/v15i130346

Sometimes, outcomes of random processes don’t seem to follow the theoretical probabilities due to the presence of bias and even when the probabilities are followed in a large number of trials, dynamic bias is still evident in many of these processes. This paper provides a short study on the bias using examples and defines what kind of processes could be biased. It also demonstrates the two types of bias which are dynamic and fixed. This study could be used to analyze the bias in various random processes and get a better understanding of the outcomes. Dynamic bias has further been explained with the help of 52 cards. The study helps in providing a better understanding of randomness and further helps in designing experiments.

##### On Sequential Probability Sampling Plan for a Truncated Life Tests Using Rayleigh Distribution

A. B. Zoramawa, S. U. Gulumbe

Asian Journal of Probability and Statistics, Page 1-7
DOI: 10.9734/ajpas/2021/v15i130339

This paper proposed a sequential probability sampling plan for a truncated life test using a Rayleigh distribution from  a designed double sampling plans where the interest was to obtain the minimum sample size necessary to assure that the average life time of a product is longer than the default life time at the specified consumer’s and producer’s confidence level. Estimations of minimum sample, acceptance and rejection numbers obtained are analyzed and presented to explain the usefulness of sequential plans in relation to single and double sampling plan. Probability of acceptance (Pa), Average sample number (ASN) and Average outgoing quality (AOQ) for the plans are computed. The three regions; acceptance, continue sampling and rejection were determined. The five points necessary to plot ASN curve were also computed and presented.

##### Incidental Parameters Problem: The Case of Gompertz Model

Ismaila A. Bolarinwa, Bushirat T. Bolarinwa

Asian Journal of Probability and Statistics, Page 8-14
DOI: 10.9734/ajpas/2021/v15i130344

The order of bias of the fixed effects gompertz model is studied, using Monte Carlo approach. Performance criteria are bias and root mean squared errors. For fixed N, bias is found to decrease steadily between T=5 and T=20 but exhibits a mixture of increase and decline afterwards. At each value of T involved, bias steadily decreases with increased value of N. Bias is found to be at most 123%, due to the combination of minimum of each of N and T involved. Decrease in order of bias is found to be more definite with increased N at fixed T than with increased T at fixed N.

##### Max Weibull-G Power Series Distributions

Munteanu Bogdan Gheorghe

Asian Journal of Probability and Statistics, Page 15-29
DOI: 10.9734/ajpas/2021/v15i130345

Based on the Weibull-G Power probability distribution family, we have proposed a new family of probability distributions, named by us the Max Weibull-G power series distributions, which may be applied in order to solve some reliability problems. This implies the fact that the Max Weibull-G power series is the distribution of a random variable max (X1 ,X2 ,...XN) where X1 ,X2 ,... are Weibull-G distributed independent random variables and N is a natural random variable the distribution of which belongs to the family of power series distribution. The main characteristics and properties of this distribution are analyzed.

##### The Iwok-Nwikpe Distribution: Statistical Properties and Its Application

Iwok Iberedem Aniefiok, Barinaadaa John Nwikpe

Asian Journal of Probability and Statistics, Page 35-45
DOI: 10.9734/ajpas/2021/v15i130347

In this paper, a new continuous probability distribution named Iwok-Nwikpe distribution is proposed. Some essential statistical properties of the proposed probability distribution have been derived. The graphs of the survival function, probability density function (p.d.f) and cumulative distribution function (c.d.f) were plotted at different values of the parameter. The mathematical expression for the moment generating function (mgf) was derived. Consequently, the first three crude moments were obtained; the distribution of order statistics, the second and third moments corrected for the mean have also been derived. The parameter of the Iwok-Nwikpe distribution was estimated by means of maximum likelihood technique. To establish the goodness of fit of the Iwok-Nwikpe distribution, three real data sets from engineering and medical science were fitted to the distribution. Findings of the study revealed that the Iwok-Nwikpe distribution performed better than the one parameter exponential distribution and other competing models used for the study.