Journal of Statistical Sciences

A New Generalized Exponential-Logarithmic Lifetime Distribution

Mohamad Babazadeh

In this paper, a new three-parameter lifetime distribution is introduced by combining an extended exponential distribution with a logarithmic distribution. This flexible distribution has increasing, decreasing and upside-down bathtub failure rate shapes. Various properties of the proposed distribution are discussed. The estimation of the parameters attained by EM algorithm and their asymptotic variance and covariance are obtained. In order to assess the accuracy of the approximation of variance and covariance of the maximum likelihood estimator, a simulation study is presented to illustrate the properties of distribution.

Ruin Probability of Individual Risk Process of Insurance Company with Dependent Claims

Abouzar Bazyari

In the individual risk processes of an insurance company with dependent claim sizes, determination of the ruin probability and time to ruin are very important. Exact computing of theses probabilities, because of it's complex structure, is not easy. In this paper, Monte Carlo simulation method is used to obtain the ruin probabilities estimates, times to ruin and confidence interval for the ruin probability estimates of the mentioned process for different dependence level of claims. In this simulation the multivariate Frank copula function and Marshall and Olkin's algorithm are provided to generate the dependent claims. Then it has shown that with increasing the dependence level of claim sizes the ruin probability of the risk process increases, while its time to ruin decreases

The Variance Estimation of Calibration Estimators of Population Total under an Unknown Population Total for Auxiliary Variables

Ebrahim Khodaie

Sampling weights are calibrated according to the theory of calibration when the sum of population total for auxiliary variables is known. Under known population, totals for auxiliary variables and some conditions Devile and Sarndal showed that generalized regression estimators could approximate calibration estimators and their variances. In this paper, under unknown population totals for auxiliary variables, an estimator for the population total is proposed and its variance is obtained. It is shown that our estimator for the population total is more efficient than the Horvitz-Thompson estimators by theoretically and simulation results.

Numerical Comparison of Some Phi-divergence Measures for Generalized Farlie Gumbel Morgenstern Copulas

Mohammad Amini

This paper explores the optimal criterion for comparison of some Phi-divergence measures. The dependence for generalized Farlie Gumbel Morgenstern family of copulas is numerically calculated and it has been shown that the Hellinger measure is the optimal criterion for measuring the divergence from independence.

Weibull Frailty Model in Survival Analysis: An Application to Colorectal Cancer Patients

Ebrahim Hajizadeh

The survival analysis methods are usually conducted based on assumption that the population is homogeneity. However, generally, this assumption in most cases is unrealistic, because of unobserved risk factors or subject specific random effect. Disregarding the heterogeneity leads to unbiased results. So frailty model as a mixed model was used to adjust for uncertainty that cannot be explained by observed factors in survival analysis. In this paper, family of power variance function distributions that includes gamma and inverse Gaussian distribution were introduced and evaluated for frailty effects. Finally the proportional hazard frailty models with Weibull baseline hazard as a parametric model used for analyzing survival data of the colorectal cancer patients.

Bayesian Estimation of the Parameters of Skew Normal Distribution

Anoshirvan Kazemnejad

Skew Normal distribution is important in analyzing non-normal data. The probability density function of skew Normal distribution contains integral function which tends researchers to some problems. Because of this problem, in this paper a simpler Bayesian approach using conditioning method is proposed to estimate the parameters of skew Normal distribution. Then the accuracy of this metrology is compared with ordinary Bayesian method in a simulation study.

General Location Model for Correlated Nominal Continuous and Ordinal Responses

Sayedeh Fatemeh Miri

In this paper a general model is proposed for the joint distribution of nominal, ordinal and continuous variables with and without missing data. Closed forms are presented for likelihood functions of general location models. Also the Joe approximation is used for the parameters of general location models with mixed continuous, ordinal and nominal data with non-ignorable missing responses. To explain the ability of proposed models some simulation studies are performed and some real data are analyzed from a foreign language achievement study.