Journal of Probability and Statistics
http://www.i-scholar.in/index.php/jps
Journal of Probability and Statistics is a peer-reviewed, open access journal that publishes original research articles as well as review articles in all areas of probability and statistics.Hindawi Limiteden-USJournal of Probability and Statistics1687-952XApplications of Fuss-Catalan Numbers to Success Runs of Bernoulli Trials
http://www.i-scholar.in/index.php/jps/article/view/97911
In a recent paper, the authors derived the exact solution for the probability mass function of the geometric distribution of order κ, expressing the roots of the associated auxiliary equation in terms of generating functions for Fuss-Catalan numbers. This paper applies the above formalism for the Fuss-Catalan 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 r ≥ 1 occurrences of success runs of length κ with ℓ-overlapping. The case ℓ < 0, where there must be a gap of at least |ℓ| trials between success runs, is also studied. Next we treat the distribution of the waiting time for the rth nonoverlapping appearance of a pair of successes separated by at most κ−2 failures (κ ≥ 2).S. J. DilworthS. R. Mane2016On a Power Transformation of Half-Logistic Distribution
http://www.i-scholar.in/index.php/jps/article/view/97912
A new continuous distribution on the positive real line is constructed from half-logistic distribution, using a transformation and its analytical characteristics are studied. Some characterization results are derived. Classical procedures for the estimation of parameters of the new distribution are discussed and a comparative study is done through numerical examples. Further, different families of continuous distributions on the positive real line are generated using this distribution. Application is discussed with the help of real-life data sets.S. D. Krishnarani2016Properties of Matrix Variate Confluent Hypergeometric Function Distribution
http://www.i-scholar.in/index.php/jps/article/view/97915
We study matrix variate confluent hypergeometric function kind 1 distributionwhich is a generalization of the matrix variate gamma distribution.We give several properties of this distribution.We also derive density functions of X<sub>2</sub><sup>−1/2</sup> X<sub>1</sub> X<sub>2</sub><sup>−1/2</sup> , (X<sub>1</sub> +X<sub>2</sub>)<sup>−1/2</sup>X<sub>1</sub>(X<sub>1</sub>+ X<sub>2</sub>)<sup>−1/2</sup>, and X<sub>1</sub>+X<sub>2</sub>, where m×m independent random matrices X<sub>1</sub>and X<sub>2</sub>follow confluent hypergeometric function kind 1 and gamma distributions, respectively.Arjun K. GuptaDaya K. NagarLuz Estela Sanchez2016Variable Selection and Parameter Estimation with the Atan Regularization Method
http://www.i-scholar.in/index.php/jps/article/view/97919
Variable selection is fundamental to high-dimensional statistical modeling. Many variable selection techniques may be implemented by penalized least squares using various penalty functions. In this paper, an arctangent type penalty which very closely resembles l<sub>0</sub> penalty is proposed; we call it Atan penalty. The Atan-penalized least squares procedure is shown to consistently select the correct model and is asymptotically normal, provided the number of variables grows slower than the number of observations. The Atan procedure is efficiently implemented using an iteratively reweighted Lasso algorithm. Simulation results and data example show that the Atan procedure with BIC-type criterion performs very well in a variety of settings.Yanxin WangZhu Li2016General Results for the Transmuted Family of Distributions and New Models
http://www.i-scholar.in/index.php/jps/article/view/97923
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 transmuted-G family density function as a linear mixture of the G and exponentiated- G densities. We investigate the asymptotes and shapes and obtain explicit expressions for the ordinary and incomplete moments, quantile and generating functions, mean deviations, Renyi 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 BourguignonIndranil GhoshGauss M. Cordeiro2016Classical and Bayesian Approach in Estimation of Scale Parameter of Nakagami Distribution
http://www.i-scholar.in/index.php/jps/article/view/97924
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 AhmadS. P. AhmadA. Ahmed2016Scan Statistics for Detecting High-Variance Clusters
http://www.i-scholar.in/index.php/jps/article/view/97926
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 high-variability income in France and then for residuals exhibiting higher variance in a linear regression context.Lionel Cucala2016