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Probabilistic properties of Cox processes of relevance for statistical modeling and inference are studied. Particularly, we study the most important classes of Cox processes, including log Gaussian Cox processes, shot noise Cox processes, and permanent Cox processes. We consider moment properties and point process operations such as thinning, displacements, and superpositioning. We also discuss how to simulate specific Cox processes.

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In many industrial experiments involving lifetimes of machines or units, experiments have to be terminated early or the number of experiments must be limited due to a variety of circumstances (e.g. when expensive, etc.) the samples that arise from such experiments are called censored data.

Cohen (1991) was one of the earliest to study a more general censoring scheme called progressive censoring scheme. The progressive Type-II censoring scheme, after starting the life-testing experiment with ....[To continue please click here]

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In spatial statistic, the data analyzed which is correlated and this correlation is due to their locations in the studied region. Such correlation that is related to distance between observations is called spatial correlation. Usually in spatial data analysis, the prediction of the amount of uncertain quantity in arbitrary 4locations of the area is considered according to attained observations from sampling points. Thus, supposing being certain the sample size, it is necessary to select a sampling design which its observations are attained from the best prediction in mentioned points that is called spatial sampling design for prediction. In this paper, the determination of such design is considered.

For this, suppose that ... [To continue please click here]

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The mixture of Type I and Type II censoring schemes, called the hybrid censoring. This article presents the statistical inferences on lognormal parameters when the data are hybrid censored. We obtain the maximum likelihood estimators (MLEs) and the approximate maximum likelihood estimators (AMLEs) of the unknown parameters. Asymptotic distributions of the maximum likelihood estimators are used to construct approximate confidence intervals. Monte Carlo simulations are performed to compare the performances of the different methods and one data set is analyzed for illustrative purposes.

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In this paper, we discuss different predictors of times to failure of units censored in a hybrid censored sample from exponential distribution. Bayesian and non-Bayesian point predictors for the times to failure of units are obtained. Non-Bayesian prediction Intervals are obtained based on pivotal and highest conditional density methods. Bayesian prediction intervals are also proposed. One real data set has been analyzed to illustrate all the prediction methods. Finally, different prediction methods have been compared using Monte Carlo simulations.

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In this paper, we discuss the statistical inference on the unknown parameters and reliability function of type-II extreme value (EVII) distribution when the observed data are progressively type-II censored. By applying EM algorithm, we obtain maximum likelihood estimates (MLEs). We also suggest approximate maximum likelihood estimators (AMLEs), which have explicit expressions. We provide Bayes estimates using both the symmetric and asymmetric loss functions via squared error loss, LINEX loss, and general entropy loss functions. Bayes estimates are obtained using the idea of Lindley and Markov chain Monte Carlo techniques. Finally, Monte Carlo simulations are presented to illustrate the methods discussed in this paper. Analysis is also carried out for a real data set.

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In this paper, we consider the estimation of the unknown parameter of the scaled logistic distribution on the basis of record values. The maximum likelihood method does not provide an explicit estimator for the scale parameter. In this article, we present a simple method of deriving an explicit estimator by approximating the likelihood function. Bayes estimator is obtained using importance sampling. Asymptotic confidence intervals, bootstrap confidence interval and credible interval are also proposed. Monte Carlo simulations are performed to compare the different proposed methods. Analysis of one real data set is also given for illustrative purposes.

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This paper proposes a simple goodness-of-fit test based on the sample covariance. It is shown that this test is preferable for alternatives of increasing and unimodal failure rate. Critical values for various sample sizes are determined by means of Monte Carlo simulations.

We compare the test based on the sample covariance with tests based on Hoeffding's maximum correlation. The usefulness of the proposed test is shown for a real example.

An empirical power study shows that the new test has the same level or upper level of performance than the best exponentiality tests in the statistical literature.

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 In this paper, we discuss different estimators of the records Weibull distribution parameters and also we apply the Kullback-Leibler divergence of survival function method to estimate record Weibull parameters. Finally, these estimators have been compared using Monte Carlo simulation and suggested good estimators.

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In this paper, we introducte a family of univariate Birnbaum-Saunders distributions arising from the skew-normal-t  distribution. We obtain several properties of this distribution such as its moments, the maximum likelihood estimation procedure via an EM-algorithm and a method to evaluate standard errors using the EM-algorithm. Finally, we apply these methods to a real data set to demonstrate its flexibility and conduct a simulation study to demonstrate the usefulness of this distribution when compared to the ordinary Birnbaum-Saunders and skew-normal Birnbaum-Saunders distributions.

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‎Abstract: This paper considers the estimation of the stress-strength parameter, say R, based on two independent Type-I progressively hybrid censored samples from exponential populations with different parameters. The maximum likelihood estimator and asymptotic confidence interval for R are obtained. Bayes estimator of R is also derived under the assumption of independent gamma priors. A Monte Carlo simulation study is used to evaluate the performance of maximum likelihood estimator, Bayes estimator and asymptotic confidence interval. Finally, a pair of real data sets is analyzed for illustrative purposes.

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Abstract: The exponential distribution is a popular model in applications to real data. We propose a new extension of this distribution, called the Lomax-exponential distribution, which presents greater flexibility to the model. Also there is a simple relation between the Lomax-exponential distribution and the Lomax distribution. Results for moment, limit behavior, hazard function, Shannon entropy and order statistic are provided. To estimate the model parameters, the method of maximum likelihood and Bayse estimations are proposed. Two data sets are used to illustrate the applicability of the Lomax-exponential distribution.

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In this paper, the problem of predicting times to failure of units censored in multiple stages of progressively hybrid censoring for the proportional hazards family is considered. We discuss different classical predictors. The best unbiased predictor ($BUP$), the maximum likelihood predictor ($MLP$) and conditional median predictor ($CMP$) are all derived. As an example, the obtained results are computed for exponential distribution. A numerical example is presented to illustrate the prediction methods discussed here. Using simulation studies, the predictors are compared in terms of bias and mean squared prediction error ($MSPE$).
 

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In this paper, we consider a new class of bivariate copulas and study their measures of association. Specifically, we propose a bivariate copula based distribution and obtain explicit expressions for the corresponding marginal and joint distributions of concomitants of generalized order statistics. Using these results, we provide the minimum variance linear unbiased estimator for the location and scale parameters of the concomitants of order statistics of Burr and logistic distributions. Then, we introduce a class of absolutely continuous bivariate distributions whose univariate margins are exponential distributions. In addition, we discuss their properties such as moment generating function, stress-strength probability and reliability of two component systems. Monte Carlo simulations are performed to highlight properties of the parameters estimates. Finally, we analyze two data sets to illustrate the flexibility and potential of the proposed distribution compared to several competing models.

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‎The estimation of R=P(X  

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In this article, we study parameter estimation of the logarithmic series distribution. A well-known method of estimation is the maximum likelihood estimate (MLE) and this method for this distribution resulted in a biased estimator for the small sample size datasets. The goal here is to reduce the bias and root mean square error of MLE of the unknown parameter. Employing the Cox and Snell method, a closed-form expression for the bias-reduction of the maximum likelihood estimator of the parameter is obtained. Moreover, the parametric Bootstrap bias correction of the maximum likelihood estimator is studied. The performance of the proposed estimators is investigated via Monte Carlo simulation studies. The numerical results show that the analytical bias-corrected estimator performs better than bootstrapped-based estimator and MLE for small sample sizes. Also, certain useful characterizations of this distribution are presented. An example via a real dataset is presented for the illustrative purposes.
 
 
 
 

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In this paper, for the first time, the upper truncated inverse Weibull (UTIW) distribution is proposed for modeling wind speed data.
Since there is a upper limit for empirical wind speed data, this data can be represented by using the UTIW distribution. In this study, the UTIW distribution is introduced and some of its statistical properties are studied. Then, the parameters of this distribution are estimated by using different methods. Simulation studies for these estimators are presented. In addition, the mentioned distribution performance is tested on real wind speed data of Ardabil province in Iran. Based on the results of the analysis, it is found that the presented distribution in this study for modeling wind speed data is more appropriate than recently introduced distributions. Finally, this distribution can be used as an alternative model for evaluating wind speed data.
 
 

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Population projections of small areas have attracted the attention of many researchers in applied demographics for many years. According to the suggested population policies of Iran in recent years and considering the need of different governmental agencies for having enough information about population and individual characteristics in small areas, studying and presenting an appropriate model of population projections for small areas seems more necessary than ever. Given that today not only population projections include estimating the number of populations and identifying their specific characteristics, but also more projections are likely to project different required characteristics of organizations. The present study attempts to introduce a model for population projections in small areas. In this study, "city" is considered as a small area. For the purpose of surveying population projection between two censuses in Iran, 2006 and 2011, Mahallat, a central city in this country, has been selected among many cities since its geographical area has not been changed from 1996 to 2011. Hence, the present article projects simulated synthetic population in 2011 with distinctive characteristics of 2006 population by presenting an extended model and comparing it with projected population from the existing model.

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