Estimation for Flexible Weibull Extension-Burr XII Distribution under Adaptive Type-II Progressive Censoring Scheme

In this paper, based on an adaptive Type-II progressive censoring scheme, estimation of flexible Weibull extension-Burr XII distribution is discussed. Maximum likelihood estimation and asymptotic confidence intervals of the unknown parameters are obtained. The adaptive Metropolis (AM) method is applied to carry out a Bayesian estimation procedure under symmetric and asymmetric loss functions and calculate the credible intervals. A simulation study is carried out to assess the performance of the estimators. Finally, a real life data set is used for illustration purpose.

A new Mean Deviation and Advanced Mean Deviation Techniques to Solve Multi-Objective Fractional Programming Problem Via Point-Slopes Formula

In this paper, we have proposed a new technique to find an efficient solution to fractional programming problems (FPP). The multi-objective fractional programming problem (MOFPP) is converted into multi-objective linear programming (MOLPP) utilizing the point-slopes formula for a plane, which has equivalent weights to the MOFPP. The MOLPP is diminished to a single objective linear programming problem (SOLPP) through using two new techniques for the values of the objective function and suggesting an algorithm for its solution. Finally, we obtained the optimal solution for MOFPP by solving the consequent linear programming problem (LPP). The proposed practicability is confirmed with the existing approaches, with some numerical examples and we indicated comparison with other techniques.

A Modified Chi-square Type Test for Distributional Validity with Applications to Right Censored Reliability and Medical Data

In this paper, a modified Chi-square goodness-of-fit test called the modified Bagdonavičius-Nikulin goodness-of-fit test statistic is investigated and the applied for distributional validation under the right censored case. The new modified goodness-of-fit test is presented and applied for the right censored data sets. The algorithm of the censored Barzilai-Borwein is employed via a comprehensive simulation study for assessing validity of the new test. The modified Bagdonavičius-Nikulin test is applied to four real and right censored data sets. A new distribution is compared with many other competitive distributions under the new modified Bagdonavičius-Nikulin goodness-of-fit test statistic.

The McDonald Lindley-Poisson Distribution

We propose the McDonald Lindley-Poisson distribution and derive some of its mathematical properties including explicit expressions for moments, generating and quantile functions, mean deviations, order statistics and their moments. Its model parameters are estimated by maximum likelihood. A simulation study investigates the performance of the estimates. The new distribution represents a more flexible model for lifetime data analysis than other existing models as proved empirically by means of two real data sets.

Some Model Assisted Estimators Using Functional Form Calibration Approach

The Model assisted estimators are approximately design unbiased, consistent and provides robustness in the case of large sample sizes. The model assisted estimators result in reduction of the design variance if underlying model reasonably defines the regression relationship. If the model is misspecified, then model assisted estimators might result in an increase of the design variance but remain approximately design unbiased and show robustness against model-misspecification. The well-known model assisted estimators, generalized regression estimators are members of a larger class of calibration estimators. Calibration method generates calibration weights that meet the calibration constraints and have minimum distance from the sampling design weights. By using different distance measures, classical calibration approach generates different calibration estimators but with asymptotically identical properties. The constraint of distance minimization was reduced for studying the properties of calibration estimators by proposing a simple functional form approach. The approach generates calibration weights that prove helpful to control the changes in calibration weights by using different choices of auxiliary variable’s functions. This paper is an extended work on model assisted approach by using functional form of calibration weights. Some new model assisted estimators are considered to get efficient and stabilized regression weights by introducing a control matrix. The asymptotic un-biasedness of the proposed estimators is verified and the expressions for MSE are derived in three different cases. A simulation study is done to compare and evaluate the efficiency of the proposed estimators with some existing model assisted estimators.

Calculating Fuzzy Inverse Matrix Using Linear Programming Problem: An Improved Approach

Calculating the matrix inverse is a key point in solving linear equation system, which involves complex calculations, particularly when the matrix elements are (Left and Right) fuzzy numbers. In this paper, first, the method of Kaur and Kumar for calculating the matrix inverse is reviewed, and its disadvantages are discussed. Then, a new method is proposed to determine the inverse of fuzzy matrix based on linear programming problem. It is demonstrated that the proposed method is capable of overcoming the shortcomings of the previous matrix inverse. Numerical examples are utilized to verify the performance and applicability of the proposed method.

A Novel Generator of Continuous Probability Distributions for the Asymmetric Left-skewed Bimodal Real-life Data with Properties and Copulas

This paper presents a novel two-parameter G family of distributions. Relevant statistical properties such as the ordinary moments, incomplete moments and moment generating function are derived. Using common copulas, some new bivariate type G families are derived. Special attention is devoted to the standard exponential base line model. The density of the new exponential extension can be “asymmetric and right skewed shape” with no peak, “asymmetric right skewed shape” with one peak, “symmetric shape” and “asymmetric left skewed shape” with one peak. The hazard rate of the new exponential distribution can be “increasing”, “U-shape”, “decreasing” and “J-shape”. The usefulness and flexibility of the new family is illustrated by means of two applications to real data sets. The new family is compared with many common G families in modeling relief times and survival times data sets.

On Smoothed MWSD Estimation of Mixing Proportion

The problem considered in the present paper is estimation of mixing proportions of mixtures of two (known) distributions by using the minimum weighted square distance (MWSD) method. The two classes of smoothed and unsmoothed parametric estimators of mixing proportion proposed in a sense of MWSD due to Wolfowitz(1953) in a mixture model F(x)=p (x)+(1-p) (x) based on three independent and identically distributed random samples of sizes n and , =1,2 from the mixture and two component populations. Comparisons are made based on their derived mean square errors (MSE). The superiority of smoothed estimator over unsmoothed one is established theoretically and also conducting Monte-Carlo study in sense of minimum mean square error criterion. Large sample properties such as rates of a.s. convergence and asymptotic normality of these estimators are also established. The results thus established here are completely new in the literature.

A New Extreme Value Model with Different Copula, Statistical Properties and Applications

In this article, we defined and studied a new distribution for modeling extreme value. Some of its mathematical properties are derived and analyzed. Simple types copula is employed for proposing many bivariate and multivariate type extensions. Method of the maximum likelihood estimation is employed to estimate the model parameters. Graphically, we perform the simulation experiments to assess of the finite sample behavior of the maximum likelihood estimations. Three applications are presented for measuring the flexibility of the new model is illustrated using three real data applications.

A Two Parameters Rani Distribution: Estimation and Tests for Right Censoring Data with an Application

In this paper, we developed a new distribution, namely the two parameters Rani distribution (TPRD). Some statistical properties of the proposed distribution are derived including the moments, moment-generating function, reliability function, hazard function, reversed hazard function, odds function, the density function of order statistics, stochastically ordering, and the entropies. The maximum likelihood method is used for model parameters estimation. Following the same approach suggested by Bagdonavicius and Nikulin (2011), modified chi squared goodness-of-fit tests are constructed for right censored data and some tests for right data is considered. An application study is presented to illustrate the ability of the suggested model in fitting aluminum reduction cells sets and the strength data of glass of the aircraft window.