Journal of Statistical Sciences

Quantile Based Tsallis Residual Entropy and its Divergence Measure

simindokht baratpour

Entropy plays a fundamental role in reliability and system lifetesting areas. In the recent studies, much attentions have been paid to use quantile functions properties and their applications as an alternate approac in distinguishing statistical models and analysis of data. In the present paper, quantile based residual Tsallis entropy is introduced and its properties in continuous models are investigated. Considering distributions of certain lifetime, explicit versions for quantile based residual Tsallis entropy are obtained and their properties monotonicity are studied and characterization based on this entropy is investigated. Also quantile based Tsallis divergence is introduced and quantile based residual Tsallis divergence is obtained. Finally, an estimator for the quantile based residual Tsallis entropy is introduced and its performance is investigate by study simulation.

Comparison of Variances Homogeneity Tests in Randomized Complete Block Design

Nabaz Esmailzadeh

Variances homogeneity test are mostly applied as a preliminary test to other analyses like test of equality of means. So far, several tests have been offered in randomized complete block design, that the most prevalent of them are Bartlett and Levene tests, and others are generalized kind of these two tests. The distribution of statistics for these tests are obtained asymptotically. Recently, a test has been introduced base on estimated critical values. In this paper, nine tests are examined based on estimated critical values method and their performance are evaluated with various blocks and treatment groups for normal and t-student distributions by a simulation study. The method of estimated critical values has a good performance in the type I error and a power improvement with respect to using asymptotic distribution.

A Characterization of the Pareto Distribution Based on Near-Record Observations

Masoumeh Akbari Lakeh

The Pareto distribution has many applications in economics and actuarial sciences. So far, a lot of properties of this distribution based on order data such as order statistics and records are studied. In this paper, a new version of notion of near-record observations is defined. Then, some results of characterization of Pareto distribution based on this new definition are obtained.

The Two-parameter Weighted Skew Laplace Distribution

Mehrdad Naderi

In order to construct the asymmetric models and analyzing data set with asymmetric properties, an useful approach is the weighted model. In this paper, a new class of skew-Laplace distributions is introduced by considering a two-parameter weight function which is appropriate to asymmetric and multimodal data sets. Also, some properties of the new distribution namely skewness and kurtosis coefficients, moment generating function, etc are studied. Finally, The practical utility of the methodology is illustrated through a real data collection.

Estimation of Population Density Function in Line Transect Sampling Method with Detection Functions

Abouzar Bazyari

In this article, we wish to find and select appropriate estimators for statistical population density function using line transect sampling in the present of detection functions with light and heavy tailed distributions. Also it is shown that how the type of detection function could be effective in selection of the best estimator and then we propose a unbiased estimators that has the lower variance than the existed estimators. the simulation results show that if detection functions have heavy tailed distribution, then the new estimators have least mean square error.

New Estimators of Modified Liu

Maryam Borzoei Bidgoli

One way of dealing with the problem of collinearity in linear models, is to make use of the Liu estimator. In this paper, a new estimator by generalizing the modified Liu estimator of Li and Yang (2012) has been proposed. This estimator is constructed based on a prior information of vector parameters in linear regression and the generalized estimator of Akdeniz and Kachiranlar (1995). Using the mean square error matrix criterion, we have obtained the superiority conditions Of this newly defined estimator over the generalized Liu estimator. For comparison sake, a numerical example as well as a Monte Carlo simulation study are considered.

Stochastic Comparison of Aggregate Claim Amounts Among Two Heterogeneous Portfolios

Ghobad Barmalzan

The aggregate claim amount in a particular time period is a quantity of fundamental importance for proper management of an insurance company and also for pricing of insurance coverages. In this paper, the usual stochastic order between aggregate claim amounts is discussed when the survival function of claims is a increasing and concave. The results established here complete some results of Li and Li (2016).

On Properties of Random-Weighted-k-out-of-n Systems

Rabeeollah Rahmani

Consider a system consisting of ‎n‎‎ ‎independent binary ‎components. ‎Suppose ‎that ‎each component has a random weight and the system works, at time ‏‎t, ‎if ‎the ‎sum ‎of ‎the ‎weight ‎of all ‎working ‎components ‎at ‎time ‎‎t‎‎, ‎is above ‎a pre-specified value k.‎ We ‎call ‎such a‎ ‎system ‎as ‎random-‎weighted-‎k‎‎-out-of-‎n‎‎ ‎system. ‎In ‎this ‎paper, we investigate the effect of the component weights and reliabilities on the system performance and show that the larger weights and reliabilities, the larger lifetime (with respect to the usual stochastic order). ‎We ‎also ‎show ‎that ‎the ‎best ‎‎random-‎weighted-‎k‎‎-out-of-‎n‎‎ ‎system ‎is ‎obtaind ‎when ‎the components with the ‎more ‎weights ‎have simultaneously ‎more ‎reliability. The reliability function and mean time to failure of a ‎random-‎weighted-‎k‎-out-of-‎n‎ ‎system are stated based on the reliability function of coherent systems. Furthermore, a simulation algorithm is presented to observe the mean time to failure of ‎random-‎weighted-‎k‎‎-out-of-‎n‎ ‎system.

A Realization of Using the Claims with Pareto Distribution in Risk Models of Insurance Company

Abouzar Bazyari

In this paper, it is shown that using the cliams with Pareto distribution for computing the ruin probabilities could has detriment for the heads of insurance company. With computing the relative error of these cliams it is shown that the estimation of claims mean is not suitable in insurance models. We will show that existance of claims with Pareto distribution in the excess of loss reinsurance model may be detriment for the policyholders of company. Also in this portfolio, with computing the conditional expectation of claims measure show that using the claims with Pareto distribution is not suitable in the estimation of claims. The estimation of conditional expectation of random variable of claims is computed by simulation method for some of the statistical distributions. The results are investigated with real examples.

Dynamic Quantile Inaccuracy Measure between Two Past Lifetimes

Mohammad Khorashadizadeh

This paper first introduces the Kerridge inaccuracy measure as an extension of the Shannon entropy and then the measure of past inaccuracy has been rewritten based on the concept of quantile function. Then, some characterizations results for lifetimes with proportional reversed hazard model property based on quantile past inaccuracy measure are obtained. Also, the class of lifetimes with increasing (decreasing) quantile past inaccuracy property and some of its properties are studied. In addition, via an example of real data, the application of quantile inaccuracy measure is illustrated.

Inverse-Probability Weighting and Multiple Imputation Methods for Analyzing Missing in the Response

Freshteh Osmani

Data loss and missing values is a common problem in data analysis. Therefore, it is important that by estimating missing values, the data was completed and placed in the proper path. Two approaches commonly used to deal with missing data are multiple imputation (MI) and inverse-probability weighting (IPW). In this study, a third approach which is a combination of MI and IPW will be introduced. It can be said by results of the simulation study that IPW/MI can have advantages over alternatives. Regarding the missing values in most studies, especially in the medical field, ignoring them leads to wrong analysis. So, using of robust methods to proper analysis of missing values is essential.

Variable Selection and Structure Identification in High Dimension for Partial Linear Additive Models

Mohammad Kazemi

In this paper, we introduce a two-step procedure, in the context of high dimensional additive models, to identify nonzero linear and nonlinear components. We first develop a sure independence screening procedure based on the distance correlation between predictors and marginal distribution function of the response variable to reduce the dimensionality of the feature space to a moderate scale. Then a double penalization based procedure is applied to identify nonzero and linear components, simultaneously. We conduct extensive simulation experiments and a real data analysis to evaluate the numerical performance of the proposed method.

Estimating of Spatial Covariance Function Using Block Differenced Composite Likelihood

Ali Mohammadian Mosammam

In this paper parameters of spatial covariance functions have been estimated using block composite likelihood method. In this method, the block composite likelihood is constructed from the joint densities of paired spatial blocks. For this purpose, after differencing data, large data sets are splited into many smaller data sets. Then each separated blocks evaluated separately and finally combined through a simple summation. The advantage of this method is that there is no need to inverse and to find determination of high dimensional matrices. The simulation shows that the block composite likelihood estimates as well as the pair composite likelihood. Finally a real data is analysed.

Maximum Likelihood Estimating of the Covariance Matrix of the ARMA Model Using Band Matrix

Behzad Mansouri

In this paper, using Band matrix, a method has been proposed to estimating the covariance matrix of the ARMA model and the likelihood function of the ARMA model with diagonal covariance matrix has been obtained and approximations for Kullback-Leibler and Chernoff criteria were presented. In addition, two rules for discriminating the ARMA models has been proposed. A simulation and real data sets are used to illustrate the performance of the proposed rules. Significant reduction of the calculations for large time series and low discrimination error rate are two characteristics of the proposed rules. In addition no need to normal assumption is showed in a theorem.