Journal of Statistical Sciences

Comparison of Some Different Methods for Hypothesis Test of Means of Log-Normal Populations

Kamel Abdollahnezhad

The log-normal distribution is used to describe the positive data that has skewed distribution with small mean and large variance. This distribution has application in many sciences for example medicine, economics, biology and alimentary science, etc. Comparison of means of several log-normal populations always has been in focus of researchers, but their test statistics are not easy to derive or extremely complicated for this comparisons. In this paper, the size and power of different testing methods including F-test, likelihood ratio test, generalized p-value approach and computational approach test are compared in a simulation study.

Inference for the Half-Logistic Distribution under Progressively Type II Hybrid Censored Samples

Akbar Asgharzadeh

One of the drawbacks of the type II progressive censoring scheme is that the length of the experiment can be very large. Because of that, recently a new censoring scheme named as the type II progressively hybrid censored scheme has received considerable interest among the statisticians. In this paper, the statistical inference for the half-logistic distribution is discussed based on the progressively type II hybrid censored samples. The maximum likelihood estimator, the approximate maximum likelihood estimator and the Bayes estimator of parameter using Lindley approximation and MCMC method are obtained. Asymptotic confidence intervals, Bootstrap confidence intervals and Bayesian credible intervals are obtained. Different point and interval estimators are compared using Monte Carlo simulation. A real data set is presented for illustrative purposes.

Goodness-of-fit Test Based on Shannon Entropy of k-Record Values from the Generalized

Mohsen Madadi

In this paper, first the Shannon entropy of k-record values is derived from the generalized Pareto distribution and propose goodness-of-fit tests based on this entropy. Finally, real data and a simulation study are used for analyzing the performance of this statistic.

Comparison of Optimal Replacement Times in Repairable Systems Based on Failure Rate Functions and Probability of Minimal Repair Times

Fatemeh Safaei

Consider a repairable system where two types of failures occur with different rate functions. The choice of minimal repair or replacement depends on the types of failures. The length of replacement cycle becomes optimal in terms of the cost function and the concept of discounted cost. In this paper, for two repairable systems the optimal replacement cycles are compared based on failure rate functions and probability of minimal repairs. Based on our results, one can make a decision for the period of replacement times. In order to illustrate the obtained results, numerical examples and simulation study are given.

A Method to Estimate Income Measurement Error

Marzieh Arbabi

Annual estimation of average household incomes is one of the main goals of the household income and expenditure survey in Iran. So, regarding importance of accuracy of gathered data and reasons that lead to error in measuring household income, in this paper, model-based methods are used for estimating income measurement error and adjusting sample households declared income for 2011 household income and expenditure survey.

Bivariate Maximum Entropy Density Function Under Some Measure of Entropies

Shahram Mansoury

Jaynes' principle of maximum entropy states that among all the probability distributions satisfying some constraints, one should be selected which has maximum uncertainty. In this paper, we consider the methods of obtaining maximum entropy bivariate density functions via Taneja and Burg's measure of entropy under the constraints that the marginal distributions and correlation coefficient are prescribed. Next, a numerical method is considered. Finally, each method is illustrated via a numerical example.

Sterling Polynomials and a New Generalization of Weibull- Geometric Distribution

Shahram Yaghoubzadeh

In this paper, we introduce a new five-parameters distribution with increasing, decreasing, bathtub-shaped failure rate, called as the Beta Weibull-Geometric (BWG) distribution. Using the Sterling Polynomials, the probability density function and several properties of the new distribution such as its reliability and failure rate functions, quantiles and moments, Renyi and Shannon entropies, moments of order statistics, mean residual life, reversed mean residual life are obtained. The maximum likelihood estimation procedure is presented in this paper. Also, we compare the results of fitting this distribution to some of their sub-models, using to a real data set. It is also shown that the BWG distribution fits better to this data set.