Asian Journal of Probability and Statistics

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.

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.

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.

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 ,...X_N) 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.

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.