Journal of Probability and Statistics
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The latest articles from Hindawi Publishing Corporation
© 2016 , Hindawi Publishing Corporation . All rights reserved.

Properties of Matrix Variate Confluent Hypergeometric Function Distribution
Mon, 08 Feb 2016 08:34:53 +0000
http://www.hindawi.com/journals/jps/2016/2374907/
We study matrix variate confluent hypergeometric function kind 1 distribution which is a generalization of the matrix variate gamma distribution. We give several properties of this distribution. We also derive density functions of , , and , where independent random matrices and follow confluent hypergeometric function kind 1 and gamma distributions, respectively.
Arjun K. Gupta, Daya K. Nagar, and Luz Estela Sánchez
Copyright © 2016 Arjun K. Gupta et al. All rights reserved.

General Results for the Transmuted Family of Distributions and New Models
Sun, 31 Jan 2016 11:20:12 +0000
http://www.hindawi.com/journals/jps/2016/7208425/
The transmuted family of distributions has been receiving increased attention over the last few years. For a baseline G distribution, we derive a simple representation for the transmutedG family density function as a linear mixture of the G and exponentiatedG densities. We investigate the asymptotes and shapes and obtain explicit expressions for the ordinary and incomplete moments, quantile and generating functions, mean deviations, Rényi and Shannon entropies, and order statistics and their moments. We estimate the model parameters of the family by the method of maximum likelihood. We prove empirically the flexibility of the proposed model by means of an application to a real data set.
Marcelo Bourguignon, Indranil Ghosh, and Gauss M. Cordeiro
Copyright © 2016 Marcelo Bourguignon et al. All rights reserved.

Classical and Bayesian Approach in Estimation of Scale Parameter of Nakagami Distribution
Sun, 17 Jan 2016 11:51:03 +0000
http://www.hindawi.com/journals/jps/2016/7581918/
Nakagami distribution is considered. The classical maximum likelihood estimator has been obtained. Bayesian method of estimation is employed in order to estimate the scale parameter of Nakagami distribution by using Jeffreys’, Extension of Jeffreys’, and Quasi priors under three different loss functions. Also the simulation study is conducted in R software.
Kaisar Ahmad, S. P. Ahmad, and A. Ahmed
Copyright © 2016 Kaisar Ahmad et al. All rights reserved.

Applications of FussCatalan Numbers to Success Runs of Bernoulli Trials
Tue, 12 Jan 2016 12:16:43 +0000
http://www.hindawi.com/journals/jps/2016/2071582/
In a recent paper, the authors derived the exact solution for the probability mass function of the geometric distribution of order , expressing the roots of the associated auxiliary equation in terms of generating functions for FussCatalan numbers. This paper applies the above formalism for the FussCatalan numbers to treat additional problems pertaining to occurrences of success runs. New exact analytical expressions for the probability mass function and probability generating function and so forth are derived. First, we treat sequences of Bernoulli trials with occurrences of success runs of length with overlapping. The case , where there must be a gap of at least trials between success runs, is also studied. Next we treat the distribution of the waiting time for the nonoverlapping appearance of a pair of successes separated by at most failures ().
S. J. Dilworth and S. R. Mane
Copyright © 2016 S. J. Dilworth and S. R. Mane. All rights reserved.

Scan Statistics for Detecting HighVariance Clusters
Tue, 05 Jan 2016 07:59:40 +0000
http://www.hindawi.com/journals/jps/2016/7591680/
Scan statistics are mostly used to detect spatial areas or time intervals in which the mean level of a given variable is more important. Sometimes, when this variable is continuous, there is an interest in looking for clusters in which its variability is more important. In this paper, two scan statistics are introduced for identifying clusters of values exhibiting higher variance. Like many classical scan statistics, the first one relies on a generalized likelihood ratio test whereas the second one is based on ratios of empirical variances. These methods are useful to identify spatial areas or time intervals in which the variability of a given variable is more important. In an application of the new methods, I look for geographical clusters of highvariability income in France and then for residuals exhibiting higher variance in a linear regression context.
Lionel Cucala
Copyright © 2016 Lionel Cucala. All rights reserved.

Robust Stability Best Subset Selection for Autocorrelated Data Based on Robust Location and Dispersion Estimator
Thu, 31 Dec 2015 13:08:48 +0000
http://www.hindawi.com/journals/jps/2015/432986/
Stability selection (multisplit) approach is a variable selection procedure which relies on multisplit data to overcome the shortcomings that may occur to singlesplit data. Unfortunately, this procedure yields very poor results in the presence of outliers and other contamination in the original data. The problem becomes more complicated when the regression residuals are serially correlated. This paper presents a new robust stability selection procedure to remedy the combined problem of autocorrelation and outliers. We demonstrate the good performance of our proposed robust selection method using real air quality data and simulation study.
Hassan S. Uraibi, Habshah Midi, and Sohel Rana
Copyright © 2015 Hassan S. Uraibi et al. All rights reserved.

Confidence Region Approach for Assessing Bioequivalence and Biosimilarity Accounting for Heterogeneity of Variability
Sun, 27 Dec 2015 12:04:29 +0000
http://www.hindawi.com/journals/jps/2015/298647/
For approval of generic drugs, the FDA requires that evidence of bioequivalence in average bioequivalence in terms of drug absorption be provided through the conduct of a bioequivalence study. A test product is said to be average bioequivalent to a reference (innovative) product if the 90% confidence interval of the ratio of means (after logtransformation) is totally within (80%, 125%). This approach is considered a oneparameter approach, which does not account for possible heterogeneity of variability between drug products. In this paper, we study a twoparameter approach (i.e., confidence region approach) for assessing bioequivalence, which can also be applied to assessing biosimilarity of biosimilar products. The proposed confidence region approach is compared with the traditional oneparameter approach both theoretically and numerically (i.e., simulation study) for finite sample performance.
Jianghao Li and SheinChung Chow
Copyright © 2015 Jianghao Li and SheinChung Chow. All rights reserved.

Estimating Parameters of a Probabilistic Heterogeneous Block Model via the EM Algorithm
Thu, 24 Dec 2015 10:00:52 +0000
http://www.hindawi.com/journals/jps/2015/657965/
We introduce a semiparametric block model for graphs, where the within and betweencluster edge probabilities are not constants within the blocks but are described by logistic type models, reminiscent of the 50yearold Rasch model and the newly introduced  models. Our purpose is to give a partition of the vertices of an observed graph so that the induced subgraphs and bipartite graphs obey these models, where their strongly interlaced parameters give multiscale evaluation of the vertices at the same time. In this way, a profoundly heterogeneous version of the stochastic block model is built via mixtures of the above submodels, while the parameters are estimated with a special EM iteration.
Marianna Bolla and Ahmed Elbanna
Copyright © 2015 Marianna Bolla and Ahmed Elbanna. All rights reserved.

Posterior Analysis of State Space Model with Spherical Symmetricity
Mon, 07 Dec 2015 13:10:09 +0000
http://www.hindawi.com/journals/jps/2015/612024/
The present work investigates state space model with nonnormal disturbances when the deviation from normality has been observed only with respect to kurtosis and the distribution of disturbances continues to follow a symmetric family of distributions. Spherically symmetric distribution is used to approximate behavior of symmetric nonnormal disturbances for discrete time series. The conditional posterior densities of the involved parameters are derived, which are further utilized in Gibbs sampler scheme for estimating the marginal posterior densities. The state space model with disturbances following multivariate distribution, which is a particular case of spherically symmetric distribution, is discussed.
Ranjita Pandey
Copyright © 2015 Ranjita Pandey. All rights reserved.

Polynomial Chaos Expansion Approach to Interest Rate Models
Thu, 03 Dec 2015 14:05:47 +0000
http://www.hindawi.com/journals/jps/2015/369053/
The Polynomial Chaos Expansion (PCE) technique allows us to recover a finite secondorder random variable exploiting suitable linear combinations of orthogonal polynomials which are functions of a given stochastic quantity , hence acting as a kind of random basis. The PCE methodology has been developed as a mathematically rigorous Uncertainty Quantification (UQ) method which aims at providing reliable numerical estimates for some uncertain physical quantities defining the dynamic of certain engineering models and their related simulations. In the present paper, we use the PCE approach in order to analyze some equity and interest rate models. In particular, we take into consideration those models which are based on, for example, the Geometric Brownian Motion, the Vasicek model, and the CIR model. We present theoretical as well as related concrete numerical approximation results considering, without loss of generality, the onedimensional case. We also provide both an efficiency study and an accuracy study of our approach by comparing its outputs with the ones obtained adopting the Monte Carlo approach, both in its standard and its enhanced version.
Luca Di Persio, Gregorio Pellegrini, and Michele Bonollo
Copyright © 2015 Luca Di Persio et al. All rights reserved.

Portfolio Theory for Symmetric and Pseudoisotropic Distributions: Fund Separation and the CAPM
Tue, 01 Dec 2015 16:24:14 +0000
http://www.hindawi.com/journals/jps/2015/235452/
The shifted pseudoisotropic multivariate distributions are shown to satisfy Rossâ€™ stochastic dominance criterion for twofund monetary separation in the case with riskfree investment opportunity and furthermore to admit the Capital Asset Pricing Model under an embedding in condition if , with the betas given in an explicit form. For the symmetric subclass, the market without riskfree investment opportunity admits fund separation if , , generalizing the classical elliptical case , and we also give the precise number of funds needed, from which it follows that we cannot, except degenerate cases, have a CAPM without riskfree opportunity. For the symmetric stable subclass, the index of stability is only of secondary interest, and several common restrictions in terms of that index can be weakened by replacing it by the (no smaller) indices of symmetry/of embedding. Finally, dynamic models with intermediate consumption inherit the separation properties of the static models.
Nils Chr. Framstad
Copyright © 2015 Nils Chr. Framstad. All rights reserved.

Approximating Explicitly the MeanReverting CEV Process
Mon, 23 Nov 2015 11:09:25 +0000
http://www.hindawi.com/journals/jps/2015/513137/
We are interested in the numerical solution of meanreverting CEV processes that appear in financial mathematics models and are described as nonnegative solutions of certain stochastic differential equations with sublinear diffusion coefficients of the form where . Our goal is to construct explicit numerical schemes that preserve positivity. We prove convergence of the proposed SD scheme with rate depending on the parameter . Furthermore, we verify our findings through numerical experiments and compare with other positivity preserving schemes. Finally, we show how to treat the twodimensional stochastic volatility model with instantaneous variance process given by the above meanreverting CEV process.
N. Halidias and I. S. Stamatiou
Copyright © 2015 N. Halidias and I. S. Stamatiou. All rights reserved.

Convex and Radially Concave Contoured Distributions
Mon, 23 Nov 2015 08:02:58 +0000
http://www.hindawi.com/journals/jps/2015/165468/
Integral representations of the locally defined stargeneralized surface content measures on star spheres are derived for boundary spheres of balls being convex or radially concave with respect to a fan in . As a result, the general geometric measure representation of starshaped probability distributions and the general stochastic representation of the corresponding random vectors allow additional specific interpretations in the two mentioned cases. Applications to estimating and testing hypotheses on scaling parameters are presented, and twodimensional sample clouds are simulated.
WolfDieter Richter
Copyright © 2015 WolfDieter Richter. All rights reserved.

On Association Measures for Continuous Variables and Correction for Chance
Wed, 18 Nov 2015 07:01:16 +0000
http://www.hindawi.com/journals/jps/2015/375491/
This paper studies correction for chance for association measures for continuous variables. The set of linear transformations of Pearson’s productmoment correlation is used as the domain of the correction for chance function. Examples of measures in this set are Tucker’s congruence coefficient, Jobson’s coefficient, and Pearson’s correlation. An equivalence relation on the set of linear transformations is defined. The fixed points of the correction for chance function are characterized. It is shown that each linear transformation is mapped to the fixed point in its equivalence class.
Matthijs J. Warrens
Copyright © 2015 Matthijs J. Warrens. All rights reserved.

Statistical Tests for the Reciprocal of a Normal Mean with a Known Coefficient of Variation
Wed, 11 Nov 2015 09:38:51 +0000
http://www.hindawi.com/journals/jps/2015/723924/
An asymptotic test and an approximate test for the reciprocal of a normal mean with a known coefficient of variation were proposed in this paper. The asymptotic test was based on the expectation and variance of the estimator of the reciprocal of a normal mean. The approximate test used the approximate expectation and variance of the estimator by Taylor series expansion. A Monte Carlo simulation study was conducted to compare the performance of the two statistical tests. Simulation results showed that the two proposed tests performed well in terms of empirical type I errors and power. Nevertheless, the approximate test was easier to compute than the asymptotic test.
Wararit Panichkitkosolkul
Copyright © 2015 Wararit Panichkitkosolkul. All rights reserved.

Confidence Interval Estimation of an ROC Curve: An Application of Generalized Half Normal and Weibull Distributions
Sun, 08 Nov 2015 12:49:16 +0000
http://www.hindawi.com/journals/jps/2015/934362/
In the recent past, the work in the area of ROC analysis gained attention in explaining the accuracy of a test and identification of the optimal threshold. Such types of ROC models are referred to as bidistributional ROC models, for example Binormal, BiExponential, BiLogistic and so forth. However, in practical situations, we come across data which are skewed in nature with extended tails. Then to address this issue, the accuracy of a test is to be explained by involving the scale and shape parameters. Hence, the present paper focuses on proposing an ROC model which takes into account two generalized distributions which helps in explaining the accuracy of a test. Further, confidence intervals are constructed for the proposed curve; that is, coordinates of the curve (FPR, TPR) and accuracy measure, Area Under the Curve (AUC), which helps in explaining the variability of the curve and provides the sensitivity at a particular value of specificity and vice versa. The proposed methodology is supported by a real data set and simulation studies.
S. Balaswamy and R. Vishnu Vardhan
Copyright © 2015 S. Balaswamy and R. Vishnu Vardhan. All rights reserved.

Estimation of Population Mean in Chain RatioType Estimator under Systematic Sampling
Tue, 03 Nov 2015 07:56:27 +0000
http://www.hindawi.com/journals/jps/2015/248374/
A chain ratiotype estimator is proposed for the estimation of finite population mean under systematic sampling scheme using two auxiliary variables. The mean square error of the proposed estimator is derived up to the first order of approximation and is compared with other relevant existing estimators. To illustrate the performances of the different estimators in comparison with the usual simple estimator, we have taken a real data set from the literature of survey sampling.
Mursala Khan and Rajesh Singh
Copyright © 2015 Mursala Khan and Rajesh Singh. All rights reserved.

Some Characterization Results on Dynamic Cumulative Residual Tsallis Entropy
Thu, 29 Oct 2015 11:13:12 +0000
http://www.hindawi.com/journals/jps/2015/694203/
We propose a generalized cumulative residual information measure based on Tsallis entropy and its dynamic version. We study the characterizations of the proposed information measure and define new classes of life distributions based on this measure. Some applications are provided in relation to weighted and equilibrium probability models. Finally the empirical cumulative Tsallis entropy is proposed to estimate the new information measure.
Madan Mohan Sati and Nitin Gupta
Copyright © 2015 Madan Mohan Sati and Nitin Gupta. All rights reserved.

An Production Inventory Controlled SelfService Queuing System
Thu, 29 Oct 2015 08:59:46 +0000
http://www.hindawi.com/journals/jps/2015/505082/
We consider a multiserver Markovian queuing system where each server provides service only to one customer. Arrival of customers is according to a Poisson process and whenever a customer leaves the system after getting service, that server is also removed from the system. Here the servers are considered as a standard production inventory. Behavior of this system is studied using a threedimensional QBD process. The condition for checking ergodicity and the steady state solutions are obtained using matrix analytic method. Unlike classical queuing models, the number of servers varies in this model according to an inventory policy.
Anoop N. Nair and M. J. Jacob
Copyright © 2015 Anoop N. Nair and M. J. Jacob. All rights reserved.

Generalized Inferences about the Mean Vector of Several Multivariate Gaussian Processes
Thu, 29 Oct 2015 08:39:15 +0000
http://www.hindawi.com/journals/jps/2015/479762/
We consider in this paper the problem of comparing the means of several multivariate Gaussian processes.
It is assumed that the means depend linearly on an unknown vector parameter and that nuisance parameters appear in the covariance matrices. More precisely, we deal with the problem of testing hypotheses, as well as obtaining confidence regions for . Both methods will be based on the concepts of generalized value and generalized confidence region adapted to our context.
Pilar Ibarrola and Ricardo Vélez
Copyright © 2015 Pilar Ibarrola and Ricardo Vélez. All rights reserved.

An Ambit Stochastic Approach to Pricing Electricity Forward Contracts: The Case of the German Energy Market
Tue, 27 Oct 2015 12:57:51 +0000
http://www.hindawi.com/journals/jps/2015/626020/
We propose an ambit stochastic model to study the electricity forward prices. We provide a detailed analysis of the probabilistic properties of such model, discussing the related martingale conditions and deriving concrete implementation of it for the related underlying spot price. The latter is obtained from the forward model through a limiting argument. Furthermore, we show, also providing a concrete example, that a proper specification of these models is able to effectively forecast prices of forward contracts written on the European Energy Exchange (EEX) AG, or German Energy Exchange, market.
Luca Di Persio and Isacco Perin
Copyright © 2015 Luca Di Persio and Isacco Perin. All rights reserved.

Comparison of the Frequentist MATA Confidence Interval with Bayesian ModelAveraged Confidence Intervals
Thu, 08 Oct 2015 12:05:45 +0000
http://www.hindawi.com/journals/jps/2015/420483/
Model averaging is a technique used to account for model uncertainty, in both Bayesian and frequentist multimodel inferences. In this paper, we compare the performance of modelaveraged Bayesian credible intervals and frequentist confidence intervals. Frequentist intervals are constructed according to the modelaveraged tail area (MATA) methodology. Differences between the Bayesian and frequentist methods are illustrated through an example involving cloud seeding. The coverage performance and interval width of each technique are then studied using simulation. A frequentist MATA interval performs best in the normal linear setting, while Bayesian credible intervals yield the best coverage performance in a lognormal setting. The use of a datadependent prior probability for models improved the coverage of the modelaveraged Bayesian interval, relative to that using uniform model prior probabilities. Datadependent model prior probabilities are philosophically controversial in Bayesian statistics, and our results suggest that their use is beneficial when model averaging.
Daniel Turek
Copyright © 2015 Daniel Turek. All rights reserved.

Measurement of Interobserver Disagreement: Correction of Cohen’s Kappa for Negative Values
Wed, 30 Sep 2015 14:27:19 +0000
http://www.hindawi.com/journals/jps/2015/751803/
As measures of interobserver agreement for both nominal and ordinal categories, Cohen’s kappa coefficients appear to be the most widely used with simple and meaningful interpretations. However, for negative coefficient values when (the probability of) observed disagreement exceeds chanceexpected disagreement, no fixed lower bounds exist for the kappa coefficients and their interpretations are no longer meaningful and may be entirely misleading. In this paper, alternative measures of disagreement (or negative agreement) are proposed as simple corrections or modifications of Cohen’s kappa coefficients. The new coefficients have a fixed lower bound of −1 that can be attained irrespective of the marginal distributions. A coefficient is formulated for the case when the classification categories are nominal and a weighted coefficient is proposed for ordinal categories. Besides coefficients for the overall disagreement across categories, disagreement coefficients for individual categories are presented. Statistical inference procedures are developed and numerical examples are provided.
Tarald O. Kvålseth
Copyright © 2015 Tarald O. Kvålseth. All rights reserved.

Generalized Information for the Order Normal Distribution
Wed, 30 Sep 2015 11:33:26 +0000
http://www.hindawi.com/journals/jps/2015/385285/
This paper investigates a generalization of Fisherâ€™s entropy type information measure under the multivariate order normal distribution, related to his
measure, as well as its corresponding Shannon entropy. Certain boundaries of this information measure are also proved and discussed.
Thomas L. Toulias
Copyright © 2015 Thomas L. Toulias. All rights reserved.

Residual and Past Entropy for Concomitants of Ordered Random Variables of Morgenstern Family
Sun, 27 Sep 2015 14:15:51 +0000
http://www.hindawi.com/journals/jps/2015/159710/
For a system, which is observed at time t, the residual and past entropies measure the uncertainty about the remaining and the past life of the distribution, respectively. In this paper, we have presented the residual and past entropy of Morgenstern family based on the concomitants of the different types of generalized order statistics (gos) and give the linear transformation of such model. Characterization results for these dynamic entropies for concomitants of ordered random variables have been considered.
M. M. Mohie ELDin, M. M. Amein, Nahed S. A. Ali, and M. S. Mohamed
Copyright © 2015 M. M. Mohie ELDin et al. All rights reserved.

Robust Bayesian Regularized Estimation Based on Regression Model
Sun, 20 Sep 2015 09:41:14 +0000
http://www.hindawi.com/journals/jps/2015/989412/
The distribution is a useful extension of the normal distribution, which can be used for statistical modeling of data sets with heavy tails, and provides robust estimation. In this paper, in view of the advantages of Bayesian analysis, we propose a new robust coefficient estimation and variable selection method based on Bayesian adaptive Lasso regression. A Gibbs sampler is developed based on the Bayesian hierarchical model framework, where we treat the distribution as a mixture of normal and gamma distributions and put different penalization parameters for different regression coefficients. We also consider the Bayesian regression with adaptive group Lasso and obtain the Gibbs sampler from the posterior distributions. Both simulation studies and real data example show that our method performs well compared with other existing methods when the error distribution has heavy tails and/or outliers.
Zean Li and Weihua Zhao
Copyright © 2015 Zean Li and Weihua Zhao. All rights reserved.

Success Run Waiting Times and FussCatalan Numbers
Mon, 14 Sep 2015 13:32:19 +0000
http://www.hindawi.com/journals/jps/2015/482462/
We present power series expressions for all the roots of the auxiliary equation of the recurrence relation for the distribution of the waiting time for the first run of consecutive successes in a sequence of independent Bernoulli trials, that is, the geometric distribution of order . We show that the series coefficients are FussCatalan numbers and write the roots in terms of the generating function of the FussCatalan numbers. Our main result is a new exact expression for the distribution, which is more concise than previously published formulas. Our work extends the analysis by Feller, who gave asymptotic results. We obtain quantitative improvements of the error estimates obtained by Feller.
S. J. Dilworth and S. R. Mane
Copyright © 2015 S. J. Dilworth and S. R. Mane. All rights reserved.

On the Computation of the Survival Probability of Brownian Motion with Drift in a Closed Time Interval When the Absorbing Boundary Is a Step Function
Wed, 09 Sep 2015 07:40:00 +0000
http://www.hindawi.com/journals/jps/2015/391681/
This paper provides explicit formulae for the probability that an arithmetic or a geometric Brownian motion will not cross an absorbing boundary defined as a step function during a finite time interval. Various combinations of downward and upward steps are handled. Numerical computation of the survival probability is done quasiinstantaneously and with utmost precision. The sensitivity of the survival probability to the number and the ordering of the steps in the boundary is analyzed.
Tristan Guillaume
Copyright © 2015 Tristan Guillaume. All rights reserved.

The Concepts of Pseudo Compound Poisson and Partition Representations in Discrete Probability
Mon, 31 Aug 2015 13:28:04 +0000
http://www.hindawi.com/journals/jps/2015/189596/
The mathematical/statistical concepts of pseudo compound Poisson and partition representations in discrete probability are reviewed and clarified. A combinatorial interpretation of the convolution of geometric distributions in terms of a variant of Newton’s identities is obtained. The practical use of the twofold convolution leads to an improved goodnessoffit for a data set from automobile insurance that was up to now not fitted satisfactorily.
Werner Hürlimann
Copyright © 2015 Werner Hürlimann. All rights reserved.

The Type I Generalized HalfLogistic Distribution Based on Upper Record Values
Thu, 13 Aug 2015 13:25:55 +0000
http://www.hindawi.com/journals/jps/2015/393608/
We consider the type I generalized halflogistic distribution and derive some new explicit expressions and recurrence relations for marginal and joint moment generating functions of upper record values. Here we show the computations for the first four moments and their variances. Next we show that results for record values of this distribution can be derived from our results as special cases. We obtain the characterization result of this distribution on using the recurrence relation for single moment and conditional expectation of upper record values. We obtain the maximum likelihood estimators of upper record values and their confidence intervals. Also, we compute the maximum likelihood estimates of the parameters of upper record values and their confidence intervals. At last, we present one real case data study to emphasize the results of this paper.
Devendra Kumar, Neetu Jain, and Shivani Gupta
Copyright © 2015 Devendra Kumar et al. All rights reserved.