Journal of Statistical Sciences

A Generalized Model for Software Reliability Evaluation Based on Non-Homogeneous Poisson Process

Tahere Yaghoobi

Given the widespread usage of software systems in all aspects of modern life, the need to produce almost error free and high quality software has become more and more important. Software reliability is considered as an important approach to software quality assessment. Software reliability modeling based on non- homogeneous Poisson process is a quite successful method in software reliability engineering. In this paper, we first study the general growth model of software reliability, and then we extend the general model by considering two types of simple and complex errors, dependency between complex errors and time delay between detecting and removing complex errors. Estimating the model parameters has been done by using two failure data sets of real software projects through MATLAB software. We compare the proposed model with two existing models using various criteria. The results show that the proposed model better fits the data, providing more accurate information about the software quality.

Perspectives of Hypothesis Testing of Ordered Means in Univariate and Multivariate Normal Distributions

Abouzar Bazyari

Hypothesis testing the homogeneity of means of k univariate normal populations against the hypothesis of one sided ordered means with unknown and equal variances is considered. A new completely method to find the uniformly most powerful test at significance level α is presented based on the multivariate t distribution. Since for more than two populations finding the null distribution of test statistic is not easy, the power of test is computed and then the critical values of test statistic for different significance levels obtained. This testing method is used for real examples. Also testing homogeneity of k mean vectors against two sided ordered mean vectors of multivariate normal populations is considered. Using Monte Carlo simulation the values of classical power of test for two bivariate and trivariate normal distributions at different significance levels are compared.

Simulation of Closed Skew Normal and Closed Skew-T Distributions for Bayesian Seismic Inversion Model

Omid Karimi

Skew spatial data often are modeled by using skew Gaussian random field. The main problem is that simulations from this random field are very time consuming for some parameter values and large dimensions. Also it is impossible in some cases and requires using of an approximation methods. One a spatial statistics branch often used to determine the natural resources such as oil and gas, is analysis of seismic data by inverse model. Bayesian Gaussian inversion model commonly is used in seismic inversion that the analytical and computational can easily be done for large dimensions. But in practice, we are encountered with the variables that are asymmetric and skewed. They are modeled using skew distributions. In Bayesian Analysis of closed skew Gaussian inversion model, there is an important problem to generate samples from closed skew normal distributions. In this paper, an efficient algorithm for the realization of the Closed Skew Normal Distribution is provided with higher dimensions. Also the Closed Skew T Distribution is offered that include heavy tails in the density function and the simulation algorithm for generating samples from the Closed Skew T Distribution is provided. Finally, the discussion and conclusions are presented.

Quantile Dynamic Cumulative Residual Entropy and Characterizations of Uniform, Exponential and Pareto Distributions

Fatemeh Hooti

In this paper, the quantile function is recalled and some reliability measures are rewritten in terms of quantile function. Next, quantile based dynamic cumulative residual entropy is obtained and some of its properties are presented. Then, some characterization results of uniform, exponential and Pareto distributions based on quantile based dynamic cumulative entropy are provided. A simple estimator is also proposed and its performance is studied for exponential distribution. Finally discussion and results are presented.

The New Generalization of Weibull Distribution

Ali Doostmoradi

In this paper we propose a new distribution based on Weibull distribution. This distribution has three parameters which displays increasing, decreasing, bathtub shaped, unimodal and increasing-decreasing-increasing failure rates. Then consider characteristics of this distribution and a real data set is used to compared proposed distribution whit some of the generalized Weibull distribution.

Robust Difference Based Estimator for Partial Linear Models

Jalal Chachi

Robust linear regression is one of the most popular problems in the robust statistics community. The parameters of this method are often estimated via least trimmed squares, which minimizes the sum of the k smallest squared residuals. So, the estimation method in contrast to the common least squares estimation method is very computationally expensive. The main idea of this paper is to propose a new estimation method in partial linear models based on minimizing the sum of the k smallest squared residuals which determines the set of outlier point and provides robust estimators. In this regard, first, difference based method in estimation parameters of partial linear models is introduced. Then the method of obtaining robust difference based estimators in partial linear models is introduced which is based on solving an optimization problem minimizing the sum of the k smallest squared residuals. This method can identify outliers. The simulated example and applied numerical example with real data found the proposed robust difference based estimators in the paper produce highly accurate results in compare to the common difference based estimators in partial linear models.

Modelling Mixed Survival and Discrete Data Using Copula Function

MohammadReza Akhoond

One of the methods that in recent years has attracted the attention of many researchers for modeling multivariate mixed outcome data is using the copula function. In this paper a regression model for mixed survival and discrete outcome data based on copula function is proposed. Where the continuous variable was time and could has censored observations. For this task it is assumed that marginal distributions are known and a latent variable was used to transform discrete variable to continuous. Then by using a copula function, the joint distribution of two variables was constructed and finally the obtained model was used to model birth interval data in Ahwaz city in south-west of Iran.

A New Mean Estimator for Judgment Post Stratification by Ordering Observations in Strata

Hamed Mohamadghasemi

Judgment post stratification is a sampling strategy which uses ranking information to give more efficient statistical inference than simple random sampling. In this paper, we introduce a new mean estimator for judgment post stratification. The estimator is obtained by using ordering observations in post strata. Our simulation results indicate that the new estimator performs better than its leading competitors in the literature.

Lindley-Logarithmic Distribution: Model and Properties

Eisa Mahmoudi

In this paper we propose a new two-parameters distribution, which is an extension of the Lindley distribution with increasing and bathtub-shaped failure rate, called as the Lindley-logarithmic (LL) distribution. The new distribution is obtained by compounding Lindley (L) and Logarithmic distributions. We obtain several properties of the new distribution such as its probability density function, its failure rate functions, quantiles and moments. The maximum likelihood estimation procedure via a EM-algorithm is presented in this paper. At the end, in order to show the flexibility and potentiality of this new class, some series of real data is used to fit.

Levy type inequality and another view of the strong law of large numbers for dependent random variables

Hamid Reza NiliSani

An important inequality for distribution of maximum independent random variables is Levy inequality. In this paper, a version of this inequality for weakly negative dependent random variables will be provided. The strong law for dependent random variables has been studied by different authors. In this research, also, the weighted complete convergence for arrays of rowwise negatively dependent random variables that are stochastically bounded will be obtained. complete convergence and strong law for such random variables will result.