Pakistan Journal of Statistics and Operation Research

Improved Estimators using Exponential Function for the Population Mean in Simple and Stratified Random Samplings

CEREN UNAL — 2021-06-03

In this article, we investigated estimators with the exponential function for the estimation of the population mean in the simple and stratified random samplings. Family of estimators based on the exponential function is proposed for both sampling methods. The proposed estimators are compared with estimators in literature. Moreover, we provide an application on different data sets to demonstrate the efficiency of the proposed estimators. As a result, the proposed estimators are more efficient than other estimators in literature under the obtained conditions in theory.

Weighted Power Lomax Distribution and its Length Biased Version: Properties and Estimation Based on Censored Samples

Amal Soliman Hassan — 2021-06-03

In this paper, a weighted version of the power Lomax distribution referred to the weighted power Lomax distribution, is introduced. The new distribution comprises the length biased and the area biased of the power Lomax distribution as new models as well as containing an existing model as the length biased Lomax distribution as special model. Essential distributional properties of the weighted power Lomax distribution are studied. Maximum likelihood and maximum product spacing methods are proposed for estimating the population parameters in cases of complete and Type-II censored samples. Asymptotic confidence intervals of the model parameters are obtained. A sample generation algorithm along with a Monte Carlo simulation study is provided to demonstrate the pattern of the estimates for different sample sizes. Finally, a real-life data set is analyzed as an illustration and its length biased distribution is compared with some other lifetime distributions.

Group Acceptance Sampling Plan for Resubmitted Lots: Size Biased Lomax Distribution

Srinivasa Rao Gadde — 2021-06-03

This research reveals a group acceptance sampling plan (GASP) for lot resubmitting is designed for conditions wherein an item life is taken from the size biased Lomax distribution (SBLD). The plan parameters of the GASP are obtained by fulfilling the prefixed producer’s and consumer’s risks as per the test completion time and the number of testers. The projected plan needs a minimal sample size in comparison with the standard GASP. This proposed plan is justified with an example.

The Balakrishnan-Alpha-Beta-Skew-Normal Distribution: Properties and Applications

Sricharan Shah — 2021-06-03

In this paper, a new form of alpha-beta-skew distribution is proposed under Balakrishnan (2002) mechanism and investigated some of its related distributions. The most important feature of this new distribution is that it is versatile enough to support both unimodal and bimodal as well as multimodal behaviors of the distribution. The moments, distributional properties and some extensions of the proposed distribution have also been studied. Finally, the suitability of the proposed distribution has been tested by conducting data fitting experiment and comparing the values of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) with the values of some other related distributions. Likelihood Ratio testis used for discriminating between normal and the proposed distributions.

A New One-term Approximation to the Standard Normal Distribution

Ahmad Hanandeh — 2021-06-03

This paper deals with a new, simple one-term approximation to the cumulative distribution function (c.d.f) of the standard normal distribution which does not have closed form representation. The accuracy of the proposed approximation measured using maximum absolute error (M.S.E) and the same criteria is used to compare this approximation with the existing one-term approximation approaches available in the literature. Our approximation has a maximum absolute error of about 0.0016 and this accuracy is sufficient for most practical applications.

Generalized Lindley Family with application on Wind Speed Data

Selen Cakmakyapan — 2021-06-03

In this study we introduce a new extended class of continuous distributions named generalized Lindley family of distributions. Some properties of the new generator, including ordinary moments, quantile, generating and entropy functions, which hold for any baseline model, are presented. The method of maximum likelihood is used for estimating the model parameters. The flexibility of the new family of distributions is shown via an application on the wind speed data set. The results shows that the proposed family is better than well-known distributions including log-logistic, Burr, Dagum, Frechet, Pearson, Dagum, Lindley, Weibull and exponential distributions.

A new parametric lifetime model with modified chi-square type test for right censored validation, characterizations and different estimation methods

Haitham Yousof — 2021-06-03

A new three-parameter extension of the generalized Nadarajah-Haghighi model is introduced and studied. Some of its statistical properties are derived. Characterization results are presented. The failure rate can be "increasing", "decreasing", "bathtub", "upside-down", "upside-down-constant", "increasing-constant" or "constant". Different non-Bayesian estimation methods under uncensored scheme are considered. Numerical simulations are performed for comparing the estimation methods using different sample sizes. The censored Barzilai-Borwein algorithm is employed via a simulation study. Using the approach of the Bagdonavicius-Nikulin chi-square goodness-of-fit test for validation under the right censored data, we propose a modified chi-square goodness-of-fit test for the new model. Based on the maximum likelihood estimators on initial data, the modified Bagdonavicius-Nikulin chi-square goodness-of-fit test recovers the loss in information. The modified Bagdonavicius-Nikulin test for validation under the right censored data is applied to four real and right censored data sets. The new model is compared with many other competitive models by means of a real data set.

A Full-Newton Step Interior Point Method for Fractional Programming Problem Involving Second Order Cone Constraint

Mansour Saraj — 2021-06-03

Some efficient interior-point methods (IPMs) are based on using a self-concordant barrier function related to the feasibility set of the underlying problem.
Here, we use IPMs for solving fractional programming problems involving second order cone constraints. We propose a logarithmic barrier function to show the self concordant property and present an algorithm to compute $\varepsilon-$solution of a fractional programming problem. Finally, we provide a numerical example to illustrate the approach.

Testing the proportionality assumption for specified covariate in the cox model

HAFDI Mohamed Ali — 2021-06-03

In this paper, I propose a test for proportional hazards assumption for specified covariates. The test
is based on a general alternative in sense that hazards rates under different values of covariates the
rate is not only constant as in the Cox model, but it may cross, go away, and may be monotonic
with time. The limit distribution of the test statistic is derived. Finite samples properties of the
test power are analyzed by simulation. Application of the proposed test on Real data examples are
considered.

The Transmuted Inverted Nadarajah-Haghighi Distribution With an Application to Lifetime Data

Aliyeh Toumaj — 2021-06-03

In this paper, we propose a new lifetime distribution. We discuss several mathematical properties of the new distribu- tion. Certain characterizations of the new distribution are provided. We study the maximum likelihood estimation and asymptotic interval estimation of the unknown parameters. A simulation study, as well as an application of the new distribution to failure data, are also presented. We end the paper with a number of remarks.

Classical and Bayesian inference approaches for the exponentiated discrete Weibull model with censored data and a cure fraction

Jorge Alberto Achcar — 2021-06-03

In this paper, we introduce maximum likelihood and Bayesian parameter estimation for the exponentiated discrete Weibull (EDW) distribution in presence of randomly right censored data. We also consider the inclusion of a cure fraction in the model. The performance of the maximum likelihood estimation approach is assessed by conducting an extensive simulation study with different sample sizes and different values for the parameters of the EDW distribution. The usefuness of the proposed model is illustrated with two examples considering real data sets.

A Novel Weighted Ensemble Method to Overcome the Impact of Under-fitting and Over-fitting on the Classification Accuracy of the Imbalanced Data Sets

Ghulam Fatima — 2021-06-03

In the data mining communal, imbalanced class dispersal data sets have established mounting consideration. The evolving field of data mining and information discovery seeks to establish precise and effective computational tools for the investigation of such data sets to excerpt innovative facts from statistics. Sampling methods re-balance the imbalanced data sets consequently improve the enactment of classifiers. For the classification of the imbalanced data sets, over-fitting and under-fitting are the two striking problems. In this study, a novel weighted ensemble method is anticipated to diminish the influence of over-fitting and under-fitting while classifying these kinds of data sets. Forty imbalanced data sets with varying imbalance ratios are engaged to conduct a comparative study. The enactment of the projected method is compared with four customary classifiers including decision tree(DT), k-nearest neighbor (KNN), support vector machines (SVM), and neural network (NN). This evaluation is completed with two over-sampling procedures, an adaptive synthetic sampling approach (ADASYN), and a synthetic minority over-sampling (SMOTE) technique. The projected scheme remained efficacious in diminishing the impact of over-fitting and under-fitting on the classification of these data sets.

On Truncated Zeghdoudi Distribution : Posterior Analysis under Different Loss Functions for Type II Censored Data

Hamida Talhi — 2021-06-03

We perform a Bayesian analysis of the upper trunacated Zeghdoudi distribution based on type II censored data. Using various loss functions including the generalised quadratic, entropy and Linex functions, we obtain Bayes estimators and the corresponding posterior risks. As tractable analytical forms of these estimators is out of reach, we propose the use of simulations based on Markov chain Monte-carlo methods to study their performance. Given nitial values of model parameters, we also obtain maximum likelihood estimators. Using Pitmanw closeness criterion and integrated mean square error we compare their performance with those of the Bayesian estimators. Finally, we illustrate our approach through an example using a set of real data.

Marshall-Olkin Lehmann Lomax Distribution: Theory, Statistical Properties, Copulas and Real Data Modeling

Mohamed Aboraya — 2021-06-03

In this work, a new four-parameter lifetime probability distribution called the Marshall-Olkin Lehmann Lomax distribution is defined and studied. The density function of the new distribution "asymmetric right skewed" and "symmetric" and the corresponding hazard rate can be monotonically increasing, increasing-constant, constant, upside down and monotonically decreasing. The coefficient of skewness can be negative and positive. We derive some new bivariate versions via Farlie Gumbel Morgenstern family, modified Farlie Gumbel Morgenstern family, Clayton Copula and Renyi's entropy.The method of maximum likelihood is used to estimate the unknown parameters. Using "biases" and "mean squared errors", a simulation study is performed for assessing the finite behavior of the maximum likelihood estimators.