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The Matusita overlapping coefficient (MOC) ???? is defined as the similarity or agreement between two distributions. Let and be two probability density functions for the two independent continuous random variables and respectively, then the MOC is defined by ???? ?? . Some studies estimated ???? under pair Weibull distributions with different scale parameters and the same shape parameter. Without using this assumption, it is difficult to find the mathematical formula of ????. This paper deals with the estimation of ???? under pair Weibull distributions without any restrictions on the parameters of the Weibull distributions. A new technique is suggested to estimate ????, which can be used with and without using any assumptions about these parameters. In all situations, the maximum likelihood method is used to estimate the Weibull distributions parameters. The properties of the resulting proposed new estimators of ???? are investigated and compared with some existing parametric and nonparametric kernel estimators via Monte-Carlo simulation technique. The results show that the new technique is very competitor and the performances of the resulting new estimators are better than that of the nonparametric kernel estimators for all considered cases.

Keywords: Matusita Overlapping Coefficient; Maximum Likelihood Method; Weibull Distribution; Relative Bias and Relative Root Mean Square Error.

MSC: 62G10

Various stochastic models were developed to predict mortality rates over the past two decade. Because of the COVID-19 Pandemic starting in 2019, the prediction accuracy by each model can be in uenced. In this paper the Poisson splitting method is implemented to calibrate parameters in the Lee-Carter(LC) Model and the Poisson Lee-Carter (PLC) Model respectively. The methodology is applied to U.S. mortality data. Mortality rates forecasts are formed for the period 2019-2020 based on data from 2000-2018. These forecasts are compared to the actual observed values to investigate the implementation of the methodology and the quality of such mortality models during the Pandemic.

Keywords: Lee-Carter Model, Poisson Lee-Carter Model, Mortality Rates Forecasts, SBS Poisson Regression Tree.

Mahalanobis distances are almost nine decades old and are extensively used in many areas of multivari- ate statistics. But there are surprisingly recent results for classical sample-based Mahalanobis distances to the centre or between individuals, such as data-independent sharp upper bounds and the fact that they become uninformative when the sample size is less than, or equal to, the number of variables plus one. It is argued here that an alternative representation of an n  p data set in the `space of variables' that associates an axis with each of the n individuals and each variable with a vector in Rn, provides an alternative setting where Mahalanobis distances have a precise geometric interpretation and where these recent results become obvious. It is shown that this setting also suggests a natural scaled Mahalanobis distance, in the interval [0; 1], which does not depend on distributional assumptions and can be used to measure the severity of an outlier. Furthermore, a direct connection is demonstrated between Maha- lanobis distances and linear regressions of certain dummy vectors in Rn on the p variables in the dataset, implying that standard linear regression subset selection algorithms will identify variables that are most responsible for large Mahalanobis distances, thereby assisting in the interpretation of outliers. Examples are discussed. Results are extended to Mahalanobis distances of the mean of a group of individuals to the centre or between means of two groups.

Keywords: Variable selection, space of variables, orthogonal projections, scaled Mahalanobis distance

MSC: 62H99, 15A99

The idea of near resolvability for balanced incomplete block design is extended to partially balanced designs and some such designs are obtained. Some series of group divisible designs, triangular designs and cyclic designs are obtained from –resolvable group divisible designs, near resolvable triangular and near resolvable cyclic designs respectively. These designs are important classes of partially balanced incomplete block designs.

Keywords: Near resolvable designs; –resolvable designs; Group divisible designs; Triangular designs; Cyclic designs; LDPC codes.

MSC: 62K10; 05B05

Estimating causal treatment eect with observational data is a challenging task since the underlying data-generating models for outcome and treatment assignment are unknown. Many widely used causal inference methods show poor operational characteristics from a statistical perspective. In this paper, we propose an ordinary least-squares (OLS) based approach for estimating causal treatment eect without parametric assumptions for either outcome or treatment assignment mechanism. Our model-free estimator builds on the nonparametric spline-based sieve estimates of two summary scores: the propensity score and the mean outcome score. We show that this proposed method leads to a p n-consistent and asymptotically normally distributed estimator of the causal treatment eect. Monte-Carlo simulation studies are conducted to compare our proposed method with other widely used conventional methods and demonstrate the superior performance of our model-free estimator. We apply this approach to a case study of the biologic anti-rheumatic treatment eect on children with newly onset juvenile idiopathic arthritis disease.

KEYWORDS: causal inference; empirical process theory; nonparametric estimation; potential outcomes; regression splines

Statistical Quality Control is an important field in production and maintenance of quality product in manufacturing environments. Reliability sampling plans are widely used in manufacturing industries to monitor the quality of products in order to safeguard both the producer and consumer which simultaneously save the cost and time of an experiment. In this article, a new lifetime distribution named as Exponential – Poisson (EP) distribution is studied. The probability of acceptance for the single sampling is designed along with its associated decision rule are given to obtain the smallest sample size for the proposed two parameter probability distribution. In this study, the specified mean lifetime is calculated and the design parameter such as sample sizes, acceptance number are determined to study the desired quality levels such as Acceptable Reliability Level (ARL), Indifference Reliability Level (IRL) and Rejectable Reliability Level (RRL), its associated OC curve and the minimum ratio values are provided for the specified producer’s risk. Table values are obtained and given for the easy selection of the plan parameters. Further, suitable illustration for the single sampling plan is given to study the plan parameters with a real time situations.

Keywords:  Exponential – Poisson (EP) Distribution, Reliability, Single Sampling Plan.