Journal of Probability and Statistics http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Subgeometric Ergodicity under Random-Time State-Dependent Drift Conditions Thu, 24 Jul 2014 00:00:00 +0000 http://www.hindawi.com/journals/jps/2014/519276/ Motivated by possible applications of Lyapunov techniques in the stability of stochastic networks, subgeometric ergodicity of Markov chains is investigated. In a nutshell, in this study we take a look at -ergodic general Markov chains, subgeometrically ergodic at rate , when the random-time Foster-Lyapunov drift conditions on a set of stopping times are satisfied. Mokaedi V. Lekgari Copyright © 2014 Mokaedi V. Lekgari. All rights reserved. An Analysis of a Heuristic Procedure to Evaluate Tail (in)dependence Mon, 21 Jul 2014 08:45:54 +0000 http://www.hindawi.com/journals/jps/2014/913621/ Measuring tail dependence is an important issue in many applied sciences in order to quantify the risk of simultaneous extreme events. A usual measure is given by the tail dependence coefficient. The characteristics of events behave quite differently as these become more extreme, whereas we are in the class of asymptotic dependence or in the class of asymptotic independence. The literature has emphasized the asymptotic dependent class but wrongly infers that tail dependence will result in the overestimation of extreme value dependence and consequently of the risk. In this paper we analyze this issue through simulation based on a heuristic procedure. Marta Ferreira and Sérgio Silva Copyright © 2014 Marta Ferreira and Sérgio Silva. All rights reserved. On -Gamma and -Beta Distributions and Moment Generating Functions Tue, 15 Jul 2014 10:08:41 +0000 http://www.hindawi.com/journals/jps/2014/982013/ The main objective of the present paper is to define -gamma and -beta distributions and moments generating function for the said distributions in terms of a new parameter . Also, the authors prove some properties of these newly defined distributions. Gauhar Rahman, Shahid Mubeen, Abdur Rehman, and Mammona Naz Copyright © 2014 Gauhar Rahman et al. All rights reserved. Two Bootstrap Strategies for a -Problem up to Location-Scale with Dependent Samples Sun, 13 Jul 2014 11:53:53 +0000 http://www.hindawi.com/journals/jps/2014/523139/ This paper extends the work of Quessy and Éthier (2012) who considered tests for the -sample problem with dependent samples. Here, the marginal distributions are allowed, under , to differ according to their mean and their variance; in other words, one focuses on the shape of the distributions. Although easily stated, this problem nevertheless requires a careful treatment for the computation of valid values. To this end, two bootstrap strategies based on the multiplier central limit theorem are proposed, both exploiting a representation of the test statistics in terms of a Hadamard differentiable functional. This accounts for the fact that one works with empirically standardized data instead of the original observations. Simulations reported show the nice sample properties of the method based on Cramér-von Mises and characteristic function type statistics. The newly introduced tests are illustrated on the marginal distributions of the eight-dimensional Oil currency data set. Jean-François Quessy and François Éthier Copyright © 2014 Jean-François Quessy and François Éthier. All rights reserved. Risk Efficiencies of Empirical Bayes and Generalized Maximum Likelihood Estimates for Rayleigh Model under Censored Data Wed, 02 Jul 2014 11:26:37 +0000 http://www.hindawi.com/journals/jps/2014/809706/ The comparison of empirical Bayes and generalized maximum likelihood estimates of reliability performances is made in terms of risk efficiencies when the data are progressively Type II censored from Rayleigh distribution. The empirical Bayes estimates are obtained using an asymmetric loss function. The risk functions of the estimates and risk efficiencies are obtained under this loss function. A real data set is presented to illustrate the proposed comparison method, and the performance of the estimates is examined and compared in terms of risk efficiencies by means of Monte Carlo simulations. The simulation results indicate that the proposed empirical Bayes estimates are more preferable than the generalized maximum likelihood estimates. Dinesh Barot and Manhar Patel Copyright © 2014 Dinesh Barot and Manhar Patel. All rights reserved. Bandwidth Selection for Recursive Kernel Density Estimators Defined by Stochastic Approximation Method Mon, 02 Jun 2014 11:55:03 +0000 http://www.hindawi.com/journals/jps/2014/739640/ We propose an automatic selection of the bandwidth of the recursive kernel estimators of a probability density function defined by the stochastic approximation algorithm introduced by Mokkadem et al. (2009a). We showed that, using the selected bandwidth and the stepsize which minimize the MISE (mean integrated squared error) of the class of the recursive estimators defined in Mokkadem et al. (2009a), the recursive estimator will be better than the nonrecursive one for small sample setting in terms of estimation error and computational costs. We corroborated these theoretical results through simulation study. Yousri Slaoui Copyright © 2014 Yousri Slaoui. All rights reserved. Sum of Bernoulli Mixtures: Beyond Conditional Independence Mon, 02 Jun 2014 09:19:24 +0000 http://www.hindawi.com/journals/jps/2014/838625/ We consider the distribution of the sum of Bernoulli mixtures under a general dependence structure. The level of dependence is measured in terms of a limiting conditional correlation between two of the Bernoulli random variables. The conditioning event is that the mixing random variable is larger than a threshold and the limit is with respect to the threshold tending to one. The large-sample distribution of the empirical frequency and its use in approximating the risk measures, value at risk and conditional tail expectation, are presented for a new class of models which we call double mixtures. Several illustrative examples with a Beta mixing distribution, are given. As well, some data from the area of credit risk are fit with the models, and comparisons are made between the new models and also the classical Beta-binomial model. Taehan Bae and Ian Iscoe Copyright © 2014 Taehan Bae and Ian Iscoe. All rights reserved. Ratio Estimator in Adaptive Cluster Sampling without Replacement of Networks Tue, 27 May 2014 06:18:30 +0000 http://www.hindawi.com/journals/jps/2014/726398/ In this paper, we study the estimators of the population total in adaptive cluster sampling by using the information of the auxiliary variable. The numerical examples showed that the ratio estimator in adaptive cluster sampling without replacement of networks is more efficient than the ratio estimators in adaptive cluster sampling without replacement of units. Nipaporn Chutiman and Monchaya Chiangpradit Copyright © 2014 Nipaporn Chutiman and Monchaya Chiangpradit. All rights reserved. A New Lifetime Distribution and Its Power Transformation Sun, 18 May 2014 00:00:00 +0000 http://www.hindawi.com/journals/jps/2014/532024/ New one-parameter and two-parameter distributions are introduced in this paper. The failure rate of the one-parameter distribution is unimodal (upside-down bathtub), while the failure rate of the two-parameter distribution can be decreasing, increasing, unimodal, increasing-decreasing-increasing, or decreasing-increasing-decreasing, depending on the values of its two parameters. The two-parameter distribution is derived from the one-parameter distribution by using a power transformation. We discuss some properties of these two distributions, such as the behavior of the failure rate function, the probability density function, the moments, skewness, and kurtosis, and limiting distributions of order statistics. Maximum likelihood estimation for the two-parameter model using complete samples is investigated. Different algorithms for generating random samples from the two new models are given. Applications to real data are discussed and compared with the fit attained by some one- and two-parameter distributions. Finally, a simulation study is carried out to investigate the mean square error of the maximum likelihood estimators, the coverage probability, and the width of the confidence intervals of the unknown parameters. Ammar M. Sarhan, Lotfi Tadj, and David C. Hamilton Copyright © 2014 Ammar M. Sarhan et al. All rights reserved. Point-Symmetric Multivariate Density Function and Its Decomposition Tue, 13 May 2014 09:21:25 +0000 http://www.hindawi.com/journals/jps/2014/597630/ For a -variate density function, the present paper defines the point-symmetry, quasi-point-symmetry of order (), and the marginal point-symmetry of order and gives the theorem that the density function is -variate point-symmetric if and only if it is quasi-point-symmetric and marginal point-symmetric of order . The theorem is illustrated for the multivariate normal density function. Kiyotaka Iki and Sadao Tomizawa Copyright © 2014 Kiyotaka Iki and Sadao Tomizawa. All rights reserved. A Study of Probability Models in Monitoring Environmental Pollution in Nigeria Mon, 05 May 2014 13:52:47 +0000 http://www.hindawi.com/journals/jps/2014/864965/ In Lagos State, Nigeria, pollutant emissions were monitored across the state to detect any significant change which may cause harm to human health and the environment at large. In this research, three theoretical distributions, Weibull, lognormal, and gamma distributions, were examined on the carbon monoxide observations to determine the best fit. The characteristics of the pollutant observation were established and the probabilities of exceeding the Lagos State Environmental Protection Agency (LASEPA) and the Federal Environmental Protection Agency (FEPA) acceptable limits have been successfully predicted. Increase in the use of vehicles and increase in the establishment of industries have been found not to contribute significantly to the high level of carbon monoxide concentration in Lagos State for the period studied. P. E. Oguntunde, O. A. Odetunmibi, and A. O. Adejumo Copyright © 2014 P. E. Oguntunde et al. All rights reserved. Estimating the Reliability Function for a Family of Exponentiated Distributions Tue, 29 Apr 2014 12:19:05 +0000 http://www.hindawi.com/journals/jps/2014/563093/ A family of exponentiated distributions is proposed. The problems of estimating the reliability function are considered. Uniformly minimum variance unbiased estimators and maximum likelihood estimators are derived. A comparative study of the two methods of estimation is done. Simulation study is preformed. Ajit Chaturvedi and Anupam Pathak Copyright © 2014 Ajit Chaturvedi and Anupam Pathak. All rights reserved. Direct Determination of Smoothing Parameter for Penalized Spline Regression Tue, 22 Apr 2014 08:49:19 +0000 http://www.hindawi.com/journals/jps/2014/203469/ Penalized spline estimator is one of the useful smoothing methods. To construct the estimator, having goodness of fit and smoothness, the smoothing parameter should be appropriately selected. The purpose of this paper is to select the smoothing parameter using the asymptotic property of the penalized splines. The new smoothing parameter selection method is established in the context of minimization asymptotic form of MISE of the penalized splines. The mathematical and the numerical properties of the proposed method are studied. First we organize the new method in univariate regression model. Next we extend to the additive models. A simulation study to confirm the efficiency of the proposed method is addressed. Takuma Yoshida Copyright © 2014 Takuma Yoshida. All rights reserved. Convergence in Distribution of Some Self-Interacting Diffusions Tue, 15 Apr 2014 16:24:39 +0000 http://www.hindawi.com/journals/jps/2014/364321/ The present paper is concerned with some self-interacting diffusions living on . These diffusions are solutions to stochastic differential equations: , where is the empirical mean of the process , is an asymptotically strictly convex potential, and is a given positive function. We study the asymptotic behaviour of for three different families of functions . If with small enough, then the process converges in distribution towards the global minima of , whereas if or if , then converges in distribution if and only if. Aline Kurtzmann Copyright © 2014 Aline Kurtzmann. All rights reserved. Increased Statistical Efficiency in a Lognormal Mean Model Mon, 14 Apr 2014 08:01:30 +0000 http://www.hindawi.com/journals/jps/2014/964197/ Within the context of clinical and other scientific research, a substantial need exists for an accurate determination of the point estimate in a lognormal mean model, given that highly skewed data are often present. As such, logarithmic transformations are often advocated to achieve the assumptions of parametric statistical inference. Despite this, existing approaches that utilize only a sample’s mean and variance may not necessarily yield the most efficient estimator. The current investigation developed and tested an improved efficient point estimator for a lognormal mean by capturing more complete information via the sample’s coefficient of variation. Results of an empirical simulation study across varying sample sizes and population standard deviations indicated relative improvements in efficiency of up to 129.47 percent compared to the usual maximum likelihood estimator and up to 21.33 absolute percentage points above the efficient estimator presented by Shen and colleagues (2006). The relative efficiency of the proposed estimator increased particularly as a function of decreasing sample size and increasing population standard deviation. Grant H. Skrepnek and Ashok Sahai Copyright © 2014 Grant H. Skrepnek and Ashok Sahai. All rights reserved. The Exponentiated Half-Logistic Family of Distributions: Properties and Applications Thu, 13 Mar 2014 12:13:19 +0000 http://www.hindawi.com/journals/jps/2014/864396/ We study some mathematical properties of a new generator of continuous distributions with two extra parameters called the exponentiated half-logistic family. We present some special models. We investigate the shapes of the density and hazard rate function. We derive explicit expressions for the ordinary and incomplete moments, quantile and generating functions, probability weighted moments, Bonferroni and Lorenz curves, Shannon and Rényi entropies, and order statistics, which hold for any baseline model. We introduce two bivariate extensions of this family. We discuss the estimation of the model parameters by maximum likelihood and demonstrate the potentiality of the new family by means of two real data sets. Gauss M. Cordeiro, Morad Alizadeh, and Edwin M. M. Ortega Copyright © 2014 Gauss M. Cordeiro et al. All rights reserved. A Software Reliability Model Using Quantile Function Tue, 11 Mar 2014 15:45:56 +0000 http://www.hindawi.com/journals/jps/2014/951608/ We study a class of software reliability models using quantile function. Various distributional properties of the class of distributions are studied. We also discuss the reliability characteristics of the class of distributions. Inference procedures on parameters of the model based on L-moments are studied. We apply the proposed model to a real data set. Bijamma Thomas, Midhu Narayanan Nellikkattu, and Sankaran Godan Paduthol Copyright © 2014 Bijamma Thomas et al. All rights reserved. An Improved Class of Chain Ratio-Product Type Estimators in Two-Phase Sampling Using Two Auxiliary Variables Thu, 06 Mar 2014 16:04:38 +0000 http://www.hindawi.com/journals/jps/2014/939701/ This paper presents a technique for estimating finite population mean of the study variable in the presence of two auxiliary variables using two-phase sampling scheme when the regression line does not pass through the neighborhood of the origin. The properties of the proposed class of estimators are studied under large sample approximation. In addition, bias and efficiency comparisons are carried out to study the performances of the proposed class of estimators over the existing estimators. It has also been shown that the proposed technique has greater applicability in survey research. An empirical study is carried out to demonstrate the performance of the proposed estimators. Gajendra K. Vishwakarma and Manish Kumar Copyright © 2014 Gajendra K. Vishwakarma and Manish Kumar. All rights reserved. A Study on the Chain Ratio-Type Estimator of Finite Population Variance Mon, 24 Feb 2014 06:53:50 +0000 http://www.hindawi.com/journals/jps/2014/723982/ We suggest an estimator using two auxiliary variables for the estimation of the unknown population variance. The bias and the mean square error of the proposed estimator are obtained to the first order of approximations. In addition, the problem is extended to two-phase sampling scheme. After theoretical comparisons, as an illustration, a numerical comparison is carried out to examine the performance of the suggested estimator with several estimators. Yunusa Olufadi and Cem Kadilar Copyright © 2014 Yunusa Olufadi and Cem Kadilar. All rights reserved. Improved Inference for Moving Average Disturbances in Nonlinear Regression Models Thu, 13 Feb 2014 09:46:24 +0000 http://www.hindawi.com/journals/jps/2014/207087/ This paper proposes an improved likelihood-based method to test for first-order moving average in the disturbances of nonlinear regression models. The proposed method has a third-order distributional accuracy which makes it particularly attractive for inference in small sample sizes models. Compared to the commonly used first-order methods such as likelihood ratio and Wald tests which rely on large samples and asymptotic properties of the maximum likelihood estimation, the proposed method has remarkable accuracy. Monte Carlo simulations are provided to show how the proposed method outperforms the existing ones. Two empirical examples including a power regression model of aggregate consumption and a Gompertz growth model of mobile cellular usage in the US are presented to illustrate the implementation and usefulness of the proposed method in practice. Pierre Nguimkeu Copyright © 2014 Pierre Nguimkeu. All rights reserved. A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator under -Mixing Dependence Sun, 19 Jan 2014 09:18:45 +0000 http://www.hindawi.com/journals/jps/2014/403764/ We consider the estimation of an unknown function for weakly dependent data (-mixing) in a general setting. Our contribution is theoretical: we prove that a hard thresholding wavelet estimator attains a sharp rate of convergence under the mean integrated squared error (MISE) over Besov balls without imposing too restrictive assumptions on the model. Applications are given for two types of inverse problems: the deconvolution density estimation and the density estimation in a GARCH-type model, both improve existing results in this dependent context. Another application concerns the regression model with random design. Christophe Chesneau Copyright © 2014 Christophe Chesneau. All rights reserved. A Batch Arrival Single Server Queue with Server Providing General Service in Two Fluctuating Modes and Reneging during Vacation and Breakdowns Wed, 08 Jan 2014 14:49:16 +0000 http://www.hindawi.com/journals/jps/2014/319318/ We study the behavior of a batch arrival queuing system equipped with a single server providing general arbitrary service to customers with different service rates in two fluctuating modes of service. In addition, the server is subject to random breakdown. As soon as the server faces breakdown, the customer whose service is interrupted comes back to the head of the queue. As soon as repair process of the server is complete, the server immediately starts providing service in mode 1. Also customers waiting for service may renege (leave the queue) when there is breakdown or when server takes vacation. The system provides service with complete or reduced efficiency due to the fluctuating rates of service. We derive the steady state queue size distribution. Some special cases are discussed and numerical illustration is provided to see the effect and validity of the results. Monita Baruah, Kailash C. Madan, and Tillal Eldabi Copyright © 2014 Monita Baruah et al. All rights reserved. Parametric Regression Models Using Reversed Hazard Rates Mon, 06 Jan 2014 09:30:22 +0000 http://www.hindawi.com/journals/jps/2014/645719/ Proportional hazard regression models are widely used in survival analysis to understand and exploit the relationship between survival time and covariates. For left censored survival times, reversed hazard rate functions are more appropriate. In this paper, we develop a parametric proportional hazard rates model using an inverted Weibull distribution. The estimation and construction of confidence intervals for the parameters are discussed. We assess the performance of the proposed procedure based on a large number of Monte Carlo simulations. We illustrate the proposed method using a real case example. Asokan Mulayath Variyath and P. G. Sankaran Copyright © 2014 Asokan Mulayath Variyath and P. G. Sankaran. All rights reserved. The Beta Generalized Half-Normal Distribution: New Properties Tue, 31 Dec 2013 14:20:42 +0000 http://www.hindawi.com/journals/jps/2013/491628/ We study some mathematical properties of the beta generalized half-normal distribution recently proposed by Pescim et al. (2010). This model is quite flexible for analyzing positive real data since it contains as special models the half-normal, exponentiated half-normal, and generalized half-normal distributions. We provide a useful power series for the quantile function. Some new explicit expressions are derived for the mean deviations, Bonferroni and Lorenz curves, reliability, and entropy. We demonstrate that the density function of the beta generalized half-normal order statistics can be expressed as a mixture of generalized half-normal densities. We obtain two closed-form expressions for their moments and other statistical measures. The method of maximum likelihood is used to estimate the model parameters censored data. The beta generalized half-normal model is modified to cope with long-term survivors may be present in the data. The usefulness of this distribution is illustrated in the analysis of four real data sets. Gauss M. Cordeiro, Rodrigo R. Pescim, Edwin M. M. Ortega, and Clarice G. B. Demétrio Copyright © 2013 Gauss M. Cordeiro et al. All rights reserved. Block Empirical Likelihood for Semiparametric Varying-Coefficient Partially Linear Errors-in-Variables Models with Longitudinal Data Sun, 29 Dec 2013 14:44:41 +0000 http://www.hindawi.com/journals/jps/2013/807135/ Block empirical likelihood inference for semiparametric varying-coeffcient partially linear errors-in-variables models with longitudinal data is investigated. We apply the block empirical likelihood procedure to accommodate the within-group correlation of the longitudinal data. The block empirical log-likelihood ratio statistic for the parametric component is suggested. And the nonparametric version of Wilk’s theorem is derived under mild conditions. Simulations are carried out to access the performance of the proposed procedure. Yafeng Xia and Hu Da Copyright © 2013 Yafeng Xia and Hu Da. All rights reserved. Estimation of Parameters of Generalized Inverted Exponential Distribution for Progressive Type-II Censored Sample with Binomial Removals Sun, 29 Dec 2013 08:36:05 +0000 http://www.hindawi.com/journals/jps/2013/183652/ We obtained the maximum likelihood and Bayes estimators of the parameters of the generalized inverted exponential distribution in case of the progressive type-II censoring scheme with binomial removals. Bayesian estimation procedure has been discussed under the consideration of the square error and general entropy loss functions while the model parameters follow the gamma prior distributions. The performances of the maximum likelihood and Bayes estimators are compared in terms of their risks through the simulation study. Further, we have also derived the expression of the expected experiment time to get a progressively censored sample with binomial removals, consisting of specified number of observations from generalized inverted exponential distribution. An illustrative example based on a real data set has also been given. Sanjay Kumar Singh, Umesh Singh, and Manoj Kumar Copyright © 2013 Sanjay Kumar Singh et al. All rights reserved. The Central Limit Theorem for th-Order Nonhomogeneous Markov Information Source Wed, 11 Dec 2013 13:34:15 +0000 http://www.hindawi.com/journals/jps/2013/645151/ We prove a central limit theorem for th-order nonhomogeneous Markov information source by using the martingale central limit theorem under the condition of convergence of transition probability matrices for nonhomogeneous Markov chain in Cesàro sense. Huilin Huang Copyright © 2013 Huilin Huang. All rights reserved. Confidence Intervals for the Coefficient of Variation in a Normal Distribution with a Known Population Mean Thu, 21 Nov 2013 13:24:06 +0000 http://www.hindawi.com/journals/jps/2013/324940/ This paper presents three confidence intervals for the coefficient of variation in a normal distribution with a known population mean. One of the proposed confidence intervals is based on the normal approximation. The other proposed confidence intervals are the shortest-length confidence interval and the equal-tailed confidence interval. A Monte Carlo simulation study was conducted to compare the performance of the proposed confidence intervals with the existing confidence intervals. Simulation results have shown that all three proposed confidence intervals perform well in terms of coverage probability and expected length. Wararit Panichkitkosolkul Copyright © 2013 Wararit Panichkitkosolkul. All rights reserved. Gaussian Estimation of One-Factor Mean Reversion Processes Sun, 20 Oct 2013 15:30:11 +0000 http://www.hindawi.com/journals/jps/2013/239384/ We propose a new alternative method to estimate the parameters in one-factor mean reversion processes based on the maximum likelihood technique. This approach makes use of Euler-Maruyama scheme to approximate the continuous-time model and build a new process discretized. The closed formulas for the estimators are obtained. Using simulated data series, we compare the results obtained with the results published by other authors. Freddy H. Marín Sánchez and J. Sebastian Palacio Copyright © 2013 Freddy H. Marín Sánchez and J. Sebastian Palacio. All rights reserved. Parameter Estimation for Type III Discrete Weibull Distribution: A Comparative Study Sat, 28 Sep 2013 14:51:26 +0000 http://www.hindawi.com/journals/jps/2013/946562/ The type III discrete Weibull distribution can be used in reliability analysis for modeling failure data such as the number of shocks, cycles, or runs a component or a structure can overcome before failing. This paper describes three methods for estimating its parameters: two customary techniques and a technique particularly suitable for discrete distributions, which, in contrast to the two other techniques, provides analytical estimates, whose derivation is detailed here. The techniques’ peculiarities and practical limits are outlined. A Monte Carlo simulation study has been performed to assess the statistical performance of these methods for different parameter combinations and sample sizes and then give some indication for their mindful use. Two applications of real data are provided with the aim of showing how the type III discrete Weibull distribution can fit real data, even better than other popular discrete models, and how the inferential procedures work. A software implementation of the model is also provided. Alessandro Barbiero Copyright © 2013 Alessandro Barbiero. All rights reserved.