q-Esscher transformed Laplace distributionH, Rimsha; George, Dais
doi: 10.1080/03610926.2018.1435812pmid: N/A
Pathway idea is a switching mechanism by which one can go from one functional form to another, and to yet another. In this paper, we introduce a q-Esscher transformed Laplace distribution, which is a stretched model for Esscher transformed Laplace distribution, obtained by introducing a new pathway parameter q, which facilitates a slow transition to the Esscher transformed Laplace distribution as q → 1. This pathway model can be obtained by optimizing Mathai’s generalized entropy with more general setup, which is a generalization of various entropy measures due to Shannon and others. The various properties of the q-Esscher transformed Laplace distribution are studied and its applications are discussed.
A new stratified three-stage unrelated randomized response model for estimating a rare sensitive attribute based on the Poisson distributionLee, Gi-Sung; Hong, Ki-Hak; Son, Chang-Kyoon
doi: 10.1080/03610926.2018.1438625pmid: N/A
This article suggests an efficient method of estimating a rare sensitive attribute which is assumed following Poisson distribution by using three-stage unrelated randomized response model instead of the Land et al. model (2011) when the population consists of some different sized clusters and clusters selected by probability proportional to size(:pps) sampling. A rare sensitive parameter is estimated by using pps sampling and equal probability two-stage sampling when the parameter of a rare unrelated attribute is assumed to be known and unknown.We extend this method to the case of stratified population by applying stratified pps sampling and stratified equal probability two-stage sampling. An empirical study is carried out to show the efficiency of the two proposed methods when the parameter of a rare unrelated attribute is assumed to be known and unknown.
Non-commutative Stein inequality and its applicationsMoslehian, Mohammad Sal; Talebi, Ali
doi: 10.1080/03610926.2018.1435813pmid: N/A
The non-commutative Stein inequality asks whether there exists a constant Cp, q depending only on p, q such that for all (positive) sequences (xn) in . The validity of (Sp, 2) for 1 < p < ∞ and (Sp, 1) for 1 ⩽ p < ∞ are known. In this paper, we verify (i) (Sp, ∞) for 1 < p ⩽ ∞; (ii) (Sp, p) for 1 ⩽ p < ∞; (iii) (Sp, q) for 1 ⩽ q ⩽ 2 and q < p < ∞. We also present some applications.
Shewhart-type nonparametric control chart for process locationZombade, D. M.; Ghute, V. B.
doi: 10.1080/03610926.2018.1435811pmid: N/A
In this paper, Shewhart-type nonparametric control chart based on run statistic is developed for monitoring the known process location of a continuous process distribution. The performance of the proposed nonparametric chart is investigated using a simulation study and is compared with sign chart and signed-rank chart and chart under normal and non-normal process distributions, using ARL and SDRL as performance measures. It is observed that the proposed nonparametric chart perform better than the chart for detecting shifts in process location under heavy tailed distribution and is a close competitor to the sign chart for normal and non-normal process distributions.
On the three-way equivalence of AUC in credit scoring with tied scoresZeng, Guoping; Zeng, Edward
doi: 10.1080/03610926.2018.1435814pmid: N/A
In credit scoring, it is well known that AUC (the area under curve) can be calculated geometrically, by the probability of a correct ranking of a good and bad pair, and by the Wilcoxon Rank-Sum statistic. This three-way equivalence was first present by Hanley and McNeil in 1982 without considering tied scores and without giving analytical proofs. In this paper, we extend the three-way equivalence to the case with tied scores and provide analytic proofs for the three-way equivalence.
Analysis of mixed correlated bivariate zero-inflated count and (k, l)-inflated beta responses with application to social network datasetsTabrizi, E.; Samani, E. Bahrami; Ganjali, M.
doi: 10.1080/03610926.2018.1435815pmid: N/A
This paper presents a new model that monitors the basic network formation mechanisms via the attributes through time. It considers the issue of joint modeling of longitudinal inflated (0, 1)-support continuous and inflated count response variables. For joint model of mentioned response variables, a correlated generalized linear mixed model is studied. The fraction response is inflated in two points k and l (k < l) and a k and l inflated beta distribution is introduced to use as its distribution. Also, the count response is inflated in zero and we use some members of zero-inflated power series distributions, hurdle-at-zero, members of zero-inflated double power series distributions and zero-inflated generalized Poisson distribution as our count response distribution. A full likelihood-based approach is used to yield maximum likelihood estimates of the model parameters and the model is applied to a real social network obtained from an observational study where the rate of the ith node’s responsiveness to the jth node and the number of arrows or edges with some specific characteristics from the ith node to the jth node are the correlated inflated (0, 1)-support continuous and inflated count response variables, respectively. The effect of the sender and receiver positions in an office environment on the responses are investigated simultaneously.
Efficient and superefficient estimators of filtered Poisson process intensitiesAlazemi, Fares; Es-Sebaiy, Khalifa; Ouknine, Youssef
doi: 10.1080/03610926.2018.1438622pmid: N/A
Let NK = {NKt, t ∈ [0, T]} be a filtered Poisson process defined on a probability space , and let θ ≔ (θt, t ∈ [0, T]) be a deterministic function which is the intensity of NK under a probability Pθ. In the present paper we prove that the natural maximum likelihood estimator (MLE) NK is an efficient estimator for θ under Pθ. Using Malliavin calculus we construct superefficient estimators of Stein type for θ which dominate, under the usual quadratic risk, the MLE NK. These superefficient estimators are given under the form where F is a random variable satisfying some assumptions and is the Malliavin derivative with respect to the compensated version of NK.
Ratio detection for mean change in α mixing observationsQin, Ruibing; Liu, Weiqi
doi: 10.1080/03610926.2018.1438623pmid: N/A
A ratio test based on the indicators of the data minus the sample median is proposed to detect the change in the mean of α-mixing stochastic sequences. The asymptotic distribution of the test is derived under the null hypothesis. The consistency of the proposed test is also obtained under the hypothesis that μ changes at some unknown time. We also propose a consistent estimator for the change point on the ratio test. Simulations demonstrate that the test and the estimator behaves well for heavy-tailed sequences. At last, an empirical application demonstrate the validity of the test and the estimator.
Slashed power-Lindley distributionIriarte, Yuri A.; Rojas, Mario A.
doi: 10.1080/03610926.2018.1438626pmid: N/A
In this article, we introduce the slashed power-Lindley distribution. This model can be seen as an extension of the power-Lindley distribution with more flexibility in terms of the kurtosis of distribution. It arises as the ratio of two independent random variables, the one being a power-Lindley distribution and a power of the uniform distribution. We present properties and carry out estimates of the model parameters by the maximum likelihood method. Finally, we conduct a small simulation study to evaluate the performance of maximum likelihood estimators and we analyze a real data set to illustrate the usefulness of the new model.