Showing papers in "Pakistan Journal of Statistics and Operation Research in 2015"
TL;DR: A new class of continuous distributions called the transmuted exponentiated generalized-G family is introduced which extends the exponentiated G class introduced by Cordeiro et al. (2013) and some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, Renyi and Shannon entropies, order statistics and probability weighted moments are derived.
Abstract: We introduce a new class of continuous distributions called the transmuted exponentiated generalized-G family which extends the exponentiated generalized-G class introduced by Cordeiro et al. (2013). We provide some special models for the new family. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, Renyi and Shannon entropies, order statistics and probability weighted moments are derived. The estimation of the model parameters is performed by maximum likelihood. The flexibility of the proposed family is illustrated by means of an applications to real dataset.
105 citations
TL;DR: In this paper, a transmuted Weibull Lomax (TWL) distribution is proposed and stutied, which generalizes the TWL distribution introduced by Tahir et al.
Abstract: A new five parameter model is proposed and stutied. The new distribution generalizes the Weibull Lomax distribution introduced by Tahir et al. (2015) and is referred to as transmuted Weibull Lomax (TWL) distribution. Various structural properties of the new model including ordinary and incomplete moments, quantiles, generating function, probability weighted moments, Renyi and q-entropies and order statistics are derived. We proposed the method of maximum likelihood for estimating the model parameters. The usefulness of the new model is illustrated through an application to a real data set.
59 citations
TL;DR: The method of maximum likelihood for estimating the model parameters and obtain the observed information matrix is proposed and various mathematical properties of the new model including ordinary and incomplete moments, quantile function, generating function and Renyi entropy are derived.
Abstract: This paper introduces a new four parameter Rayleigh distribution which generalizes the transmuted generalized Rayleigh distribution introduced by Merovci (2014). The new model is referred to as exponentiated transmuted generalized Rayleigh (ETGR) distribution. Various mathematical properties of the new model including ordinary and incomplete moments, quantile function, generating function and Renyi entropy are derived. We proposed the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. Two real data sets are used to compare the flexibility of the new model versus other models.
50 citations
TL;DR: In this article, a new distribution, the New Weibull-Pareto, is defined and studied and various properties of the distributions are obtained and the method of maximum likelihood used to estimate the parameters of the distribution.
Abstract: A new distribution, the New Weibull-Pareto, is defined and studied. Various properties of the distributions are obtained and the method of maximum likelihood used to estimate the parameters of the distribution. The usefulness of the distribution has also been demonstrated by applying it to real life data.
43 citations
TL;DR: In this paper, the impact of financial leverage on corporate financial performance of Pakistan's textile sector from 1999-2012 using panel data was examined with a special focus on the Global Financial Crisis of 2007-2008.
Abstract: The objective of this study is to investigate the impact of financial leverage on corporate financial performance of Pakistan’s textile sector from 1999-2012 using panel data. The leverage-performance relationship is examined with a special focus on the Global Financial Crisis of 2007-2008. Both accounting-based (Return on Assets - ROA) and market-based (Tobin’s Q) measures of corporate financial performance are used. Regression analysis is performed with and without inclusion of financial crisis dummy. Total Debt to Total Assets (TDTA), Long Term Debt to Total Assets (LDTA), Short Term Debt to Total Assets (SDTA) and Debt to Equity (DE) ratios are used as proxies for financial leverage whereas firm’s size and firm’s efficiency are used as control variables. The results indicate that financial leverage has a negative impact on corporate performance when measured with ROA. Whereas in case of Tobin’s Q, SDTA coefficient is positive. It can be concluded that since cost of borrowing is high in Pakistan and debt capital markets are less developed, firms are forced to resort to banks as their source of debt finance and thus have to repay huge amount of principal and interest which has a heavy toll on their financial health. In addition to this, financial crisis was found to have a negative impact on corporate performance and also affect the leverage-performance relationship.
24 citations
TL;DR: Simulation and real data results show that AEN and AAEN has advantage with small, medium, and extremely correlated variables in terms of both prediction and variable selection consistency comparing with other existing penalized methods.
Abstract: Reduction of the high dimensional binary classification data using penalized logistic regression is one of the challenges when the explanatory variables are correlated. To tackle both estimate the coefficients and perform variable selection simultaneously, elastic net penalty was successfully applied in high dimensional binary classification. However, elastic net has two major limitations. First it does not encouraging grouping effects when there is no high correlation. Second, it is not consistent in variable selection. To address these issues, an adjusted of the elastic net (AEN) and its adaptive adjusted elastic net (AAEM), are proposed to take into account the small and medium correlation between explanatory variables and to provide the consistency of the variable selection simultaneously. Our simulation and real data results show that AEN and AAEN has advantage with small, medium, and extremely correlated variables in terms of both prediction and variable selection consistency comparing with other existing penalized methods.
17 citations
TL;DR: In this paper, a new generating family of generalized distributions called the Kumaraswamy - kw-kw (KW-KW) family is presented and four important common families of distributions are illustrated as special cases from the KW KW family.
Abstract: Finding the best fitted distribution for data set becomes practically an important problem in world of data sets so that it is useful to use new families of distributions to fit more cases or get better fits than before. In this paper, a new generating family of generalized distributions so called the Kumaraswamy - Kumaraswamy (KW-KW) family is presented. Four important common families of distributions are illustrated as special cases from the KW KW family. Moments, probability weighted moments, moment generating function, quantile function, median, mean deviation, order statistics and moments of order statistics are obtained. Parameters estimation and variance covariance matrix are computed using maximum likelihood method. A real data set is used to illustrate the potentiality of the KW KW weibull distribution (which derived from the kw kw family) compared with other distributions.
16 citations
TL;DR: In this paper, the authors developed the length-biased form of Weighted Maxwell distribution (WMD) and derived the statistical properties of the derived distribution including moments, moment generating function, hazard rate, reverse hazard rate and Shannon entropy.
Abstract: The concept of length-biased distribution can be employed in development of proper models for life-time data. In this paper, we develop the length-biased form of Weighted Maxwell distribution (WMD). We study the statistical properties of the derived distribution including moments, moment generating function, hazard rate, reverse hazard rate, Shannon entropy and estimation of parameters
14 citations
TL;DR: Fences constructed by the modified technique are close to the true 95% than adjusted boxplot which proves its superiority on the existing technique.
Abstract: Tukey’s boxplot is very popular tool for detection of outliers. It reveals the location, spread and skewness of the data. It works nicely for detection of outliers when the data are symmetric. When the data are skewed it covers boundary away from the whisker on the compressed side while declares erroneous outliers on the extended side of the distribution. Hubert and Vandervieren (2008) made adjustment in Tukey’s technique to overcome this problem. However another problem arises that is the adjusted boxplot constructs the interval of critical values which even exceeds from the extremes of the data. In this situation adjusted boxplot is unable to detect outliers. This paper gives solution of this problem and proposed approach detects outliers properly. The validity of the technique has been checked by constructing fences around the true 95% values of different distributions. Simulation technique has been applied by drawing different sample size from chi square, beta and lognormal distributions. Fences constructed by the modified technique are close to the true 95% than adjusted boxplot which proves its superiority on the existing technique.
14 citations
TL;DR: In this article, the authors tried to find out the impact of eLearning perception and eLearning advantages on eLearning for stress management with eLearning For Corporate Training as a mediator.
Abstract: The objective of the study was to develop a model with and without the mediator comparing direct and indirect Impacts using Bootstrap (Two tailed significance results to be used), options for manufacturing, services sectors and overall and finding out the significance of the relationship. Study tried to find out the Impact of eLearning Perception and eLearning Advantages on eLearning for Stress Management with eLearning for Corporate Training as a mediator. This is a cross sectional study conducted in Pakistan. Detailed questionnaire was used to collect the data. Total sample size of 686 includes 331 from manufacturing sector and 355 from services sector. Study revealed that overall eLearning for corporate training partially mediates relationship between eLearning Perception and elearning for stress management. However, in subgroup of manufacturing sector full mediation is observed. eLearning for corporate training partially mediates relationship between eLearning Advantages and Stress management training. Similar partial mediation is observed for subgroups of manufacturing and services sector. However in subgroup of manufacturing sector no mediation was observed.
10 citations
TL;DR: In this paper, the impact of human resource practices on employee performance was investigated for their mediation effect on the relationship between human resources practices and employee performance and the results support that job embeddedness, perceived organization support and trust have partial or full mediation role for HR-Performance relationship of teaching faculty of higher education sector.
Abstract: The purpose of this paper is to find out the impact of Human Resource practices on employee performance. Job embeddedness, Perceived organizational support and Trust were taken as mediators and they were investigated for their mediation effect on the relationship between human resource practices and employee performance. Organizational citizenship behavior and task performance were taken as two dimensions of Employee Performance. Data was collected through questionnaires from faculty members of different campuses of Public sector University in Pakistan. Results support that job embeddedness, perceived organization support and trust have partial or full mediation role for HR-Performance relationship of teaching faculty of Higher Education sector.
TL;DR: In this paper, the identification problem of autoregressive processes from the Bayesian point of view is addressed by using three well known priors: G prior, the Natural-Conjugate prior and Jeffrey's prior.
Abstract: The main objective of the current study is to handle the identification problem of autoregressive processes from the Bayesian point of view. Two Bayesian identification approaches are considered. They are referred to as the direct and the indirect approaches. The two approaches are employed to solve the Bayesian identification problem of autoregressive processes using three well known priors. These priors are the G prior, the Natural-Conjugate prior and Jeffrey's prior. The theoretical derivations related to the two Bayesian identification approaches are conducted using the above mentioned priors. Moreover, the performance of the two techniques, using each of the three priors, is investigated via comprehensive simulation studies. Simulation results show that the two techniques are adequate to solve the identification problem of autoregressive processes. The increase in the time series length leads to better performance for each technique. The use of different priors doesn't affect the previous results.
TL;DR: In this article, a class of estimators based on information of two auxiliary variables is proposed, and the expressions of mean square errors of the proposed estimators are derived in a general form.
Abstract: This paper proposes a class of estimators based on information of two auxiliary variables. The expressions of mean square errors of the proposed class of estimators are derived in a general form. It is shown that the proposed class of estimators is always more efficient than regression estimator based on two variable, estimators proposed by Abu-Dayeh (2003) and estimators recently proposed by and Lu and Yan (2014). In addition, we support this theoretical result by an empirical study using original data to show the superiority of the constructed estimators over others.
TL;DR: In this paper, a single server Markovian queueing model is considered, where arrivals are allowed to join the queue according to a Poisson distribution and the service takes place according to an exponential distribution.
Abstract: A single server Markovian queueing model is considered. The arrivals are allowed to join the queue according to a Poisson distribution and the service takes place according to an exponential distribution. Whenever the system is empty, the server goes for a vacation and return back to the system after N or more customers are found in the system. If the number of customers in the system is less than ‘ ’ then the server takes another vacation. In this paper, we obtain explicit expressions for the time dependent system size probabilities of such a model using Laplace transform and generating function techniques. Numerical illustrations are added to support the theoretical results obtained.
TL;DR: In this paper, the distribution of order statistics of two parametric Lomax distribution is studied and the exact analytical expressions of entropy, residual entropy and past residual entropy for order statistics are derived.
Abstract: In this paper we study the distribution of order statistics of the two parametric Lomax distribution. We consider the single and product moment of order statistics from Lomax distribution. Also, we establish some recurrence relation for single moments of order statistics. The exact analytical expressions of entropy, residual entropy and past residual entropy for order statistics of Lomax distribution is derived.
TL;DR: In this article, the level of TDS in groundwater with spatial domain Tehsil Jampur, Pakistan is considered as response variable and four estimation techniques were comparatively studied for fitting well known matern spatial covariance models.
Abstract: In this research article, level of TDS in groundwater with spatial domain Tehsil Jampur, Pakistan is considered as response variable. Its enhanced level in drinking water produces both the human health concerns and aquatic ecological impacts. Its high value causes several diseases like bilestone, joints stiffness, obstruction of blood vessel and kidney stones. Some Geostatistical techniques were used to interpolate TDS at unmonitored locations of Tehsil Jampur. Four estimation techniques were comparatively studied for fitting well known matern spatial covariance models. Model based Ordinary Kriging (OK) and Bayesian Kriging (BK) were used for spatial interpolation at unmonitored locations. Cross validation statistic was used to select best interpolation technique with reduced RMSPE. Prediction maps were generated for visual presentation of interpolated sited for both techniques. This study revealed that among thirty observed locations, 56% water samples exceed the maximum permissible limit (1000g/ml) of TDS as described by WHO
TL;DR: A dynamic programming procedure to develop an optimal sequential sampling plan based on sequential iterative approach and a backward recursive algorithm is developed that can be adapted to a computer program.
Abstract: In this paper we proposed a dynamic programming procedure to develop an optimal sequential sampling plan. A suitable cost model is employed for depicting the cost of sampling, accepting or rejecting the lot. This model is based on sequential approach. A sequential iterative approach is used for modeling the cost of different decisions in each stage. In addition a backward recursive algorithm is developed that can be adapted to a computer program. At the end of this paper a numerical example is solved to show how this model works.
TL;DR: In this article, a variable quality characteristic is assumed to follow the new weibull-pareto distribution and the control limits for the respective control charts are developed based on the evaluated percentiles of sample statistic like mean, median, midrange, range and standard deviation.
Abstract: A variable quality characteristic is assumed to follow the new weibull-Pareto distribution. Based on the evaluated percentiles of sample statistic like mean, median, midrange, range and standard deviation, the control limits for the respective control charts are developed . The admissibility and power of the control limits is assessed in comparison with those based on the popular Shewhart control limits.
TL;DR: In this paper, two general classes of estimators have been suggested in two different situations of random non-response and studied their properties under two different set up of two-phase sampling.
Abstract: The present investigation deals with the problem of estimation of population variance in presence of random non-response in two-phase (double) sampling. Using information on two auxiliary variables, two general classes of estimators have been suggested in two different situations of random non-response and studied their properties under two different set up of two-phase sampling. It is shown that several estimators may be generated from our proposed classes of estimators. Proposed classes of estimators are empirically compared with some contemporary estimators of population variance under the similar realistic situations and their performances have been demonstrated through numerical illustration and graphical interpretation which are followed by suitable recommendations.
TL;DR: In this paper, a new mixture of Modified Exponential (ME) and Poisson distribution has been introduced, named as Extended Poisson Exponential distribution, which possesses increasing and decreasing failure rates.
Abstract: A new mixture of Modified Exponential (ME) and Poisson distribution has been introduced in this paper. Taking the Maximum of Modified Exponential random variable when the sample size follows a zero truncated Poisson distribution we have derived the new distribution, named as Extended Poisson Exponential distribution. This distribution possesses increasing and decreasing failure rates. The Poisson-Exponential, Modified Exponential and Exponential distributions are special cases of this distribution. We have also investigated some mathematical properties of the distribution along with Information entropies and Order statistics of the distribution. The estimation of parameters has been obtained using the Maximum Likelihood Estimation procedure. Finally we have illustrated a real data application of our distribution.
TL;DR: In this article, the authors introduce the Pakistan statistics communities to the applications of Bayesian Monte Carlo methods in the analysis of gravitational wave data with an overview of the Bayesian signal detection and estimation methods and demonstration by a couple of simplified examples.
Abstract: The Bayesian approach is increasingly becoming popular among the astrophysics data analysis communities. However, the Pakistan statistics communities are unaware of this fertile interaction between the two disciplines. Bayesian methods have been in use to address astronomical problems since the very birth of the Bayes probability in eighteenth century. Today the Bayesian methods for the detection and parameter estimation of gravitational waves have solid theoretical grounds with a strong promise for the realistic applications. This article aims to introduce the Pakistan statistics communities to the applications of Bayesian Monte Carlo methods in the analysis of gravitational wave data with an overview of the Bayesian signal detection and estimation methods and demonstration by a couple of simplified examples.
TL;DR: In this article, the suitability of Finite Mixture of von Mises Fisher (mvMF) and Circular Distribution based on Nonnegative Trigonometric Sums (NNTS) models were judged based on a graphical representation and goodness-of-fit statistics.
Abstract: Wind direction is the direction from which the wind is blowing. It is expressed in terms of degrees measured clockwise from geographical direction. The knowledge of the wind direction can be used to obtain information about the wind energy potential, dispersion of particulate matter in the air, the effects of engineering structures on the building, maritime study, and etc. This study provides a suitable model for the wind direction that indicates multi-modal distributional properties. A case study involves with a data from Kudat, Malaysia has been analysed. The statistical models known as a Finite Mixture of von Mises Fisher (mvMF) and Circular Distribution based on Nonnegative Trigonometric Sums (NNTS) has been fitted to the data. Then, the suitability of mvMF and NNTS models were judged based on a graphical representation and goodness-of-fit statistics. The results found that the mvMF model with components is sufficient to provide a best model.
TL;DR: In this article, the authors present certain characterizations of a recently introduced distribution (Afify et al., 2014), called Transmuted Complementary Weibull Geometric distribution based on: ( ) hazard function ; ( ) a simple relation between two truncated moments.
Abstract: We present certain characterizations of a recently introduced distribution (Afify et al., 2014), called Transmuted Complementary Weibull Geometric distribution based on: ( ) hazard function ; ( ) a simple relation between two truncated moments. We like to mention that the characterization ( ) which is expressed in terms of the ratio of truncated moments is stable in the sense of weak convergence. It does not require a closed form for the cumulative distribution function and serves as a bridge between a first order differential equation and probability.
TL;DR: In this article, the effect of measurement errors on the power curve of standardization procedure was studied for doubly truncated normal distribution, and a method of obtaining the expression of the power of control chart was proposed to study the sensitivity of the monitoring procedure, average run length was also considered.
Abstract: Researchers in various quality control procedures consider the possibility of measurement error effect on the power of control charts as an important issue. In this paper the effect of measurement errors on the power curve of standardization procedure will be studied for doubly truncated normal distribution. A method of obtaining the expression of the power of control chart for doubly truncated normal distribution is being proposed. The effect of truncation will be shown accordingly. To study the sensitivity of the monitoring procedure, average run length () is also considered.
TL;DR: In this article, a process capability and system availability analysis for the inverse Rayleigh lifetime distribution is discussed for the analysis of process capability with a Bayesian approach with a conjugate gamma distribution.
Abstract: In this article, process capability and system availability analysis is discussed for the inverse Rayleigh lifetime distribution. Bayesian approach with a conjugate gamma distribution is adopted for the analysis. Different types of loss functions are considered to find Bayes estimates of the process capability and system availability. A simulation study is conducted for the comparison of different loss functions.
TL;DR: In this article, a new class of skew-symmetric distributions which are formulated based on cumulative distributions of skew symmetric densities is introduced, and the probability density function and cumulative distribution function of the skew type I generalized logistic distribution denoted by S'GLD are derived.
Abstract: Generalized logistic distributions are very versatile and give useful representations of many physical situations. Skew-symmetric densities recently received much attention in the literature. In this paper, we introduce a new class of skew-symmetric distributions which are formulated based on cumulative distributions of skew-symmetric densities. We derive, the probability density function (pdf) and cumulative distribution function (CDF) of the skew type I generalized logistic distribution denoted by S'GLD . The general statistical properties of the S'GLD such as: the moment generating function (mgf), characteristic function (chf), Laplace and Fourier transformations are obtained in explicit form. Expressions for the n th moment, skewness and kurtosis are discussed. Mean deviation about the mean and about the median, Renye entropy and the order statistics are also given. We consider the general case by inclusion of location and scale parameters. The results of Nadarajah (2009) are obtained as special cases. Graphical illustration of some results has been represented. Further we present a numerical example to illustrate some results of this paper.
TL;DR: In this article, a generalization of the Laplace distribution with location parameter (theta, theta, -infty 0,$) is defined by adding a third parameter (α>0) as a shape parameter.
Abstract: A generalization of Laplace distribution with location parameter $\theta$, $\, -\infty 0,$ is defined by introducing a third parameter $\alpha>0$ as a shape parameter. One tractable class of this generalization arises when $\alpha$ is chosen such that 1/$\alpha$ is a positive integer. In this article, we derive explicit forms for the moments of order statistics, and mean values of the range, quasi--ranges, and spacings of a random sample corresponded to any member of this class. For values of the shape parameter $\alpha$ equal $1/i, i=1,\dotsb,8$, and sample sizes equal 2(1)15 short tables are computed for the exact mean values of the range, quasi--ranges, and spacings. Means and variances of all order statistics are also tabulated.
TL;DR: In this article, the problem of a three stage multivariate stratified sample survey has been formulated as a non-linear stochastic programming problem by considering survey cost and the variances as random variables.
Abstract: In this paper, we have considered the problem of three-stage sample surveys. The problem of a three stage multivariate stratified sample survey has been formulated as a non-linear stochastic programming problem by considering survey cost and the variances as random variables. The stochastic programming problem has been converted into equivalent deterministic form using Chance constraint programming and modified E-model.
TL;DR: In this paper, the quartile double ranked set sampling (QDRSS) method is considered for estimating the population median and the sample median based on QDRSS is suggested as an estimator.
Abstract: In this article, quartile double ranked set sampling (QDRSS) method is considered for estimating the population median. The sample median based on QDRSS is suggested as an estimator of the population median. The QDRSS is compared with the simple random sampling (SRS), ranked set sampling (RSS) and quartile ranked set sampling (QRSS) methods. A real data set is used for illustration. It turns out that, for the symmetric distributions considered in this study, the QDRSS estimators are unbiased of the population median and are more than their counterparts using SRS, RSS and QRSS based on the same sample number of measured units. For asymmetric distributions, QDRSS is biased and it is more efficient than SRS, QRSS for all sample size m while it is more efficient than RSS if m>4 .
Abstract: Burr type III is an important distribution used to model the failure time data. The paper addresses the problem of estimation of parameters of the Burr type III distribution based on maximum likelihood estimation (MLE) when the samples are left censored. As the closed form expression for the MLEs of the parameters cannot be derived, the approximate solutions have been obtained through iterative procedures. An extensive simulation study has been carried out to investigate the performance of the estimators with respect to sample size, censoring rate and true parametric values. A real life example has also been presented. The study revealed that the proposed estimators are consistent and capable of providing efficient results under small to moderate samples.