Higher-order expansions of powered extremes of logarithmic general error distribution

In this paper,Let M_(n)denote the maximum of logarithmic general error distribution with parameter v≥1.Higher-order expansions for distributions of powered extremes M_(n)^(p)are derived under an optimal choice of normalizing constants.It is shown that M_(n)^(p),when v=1,converges to the Frechet extreme value distribution at the rate of 1/n,and if v>1 then M_(n)^(p)converges to the Gumbel extreme value distribution at the rate of(loglogn)^(2)=(log n)^(1-1/v).

Distributional expansion of maximum from logarithmic general error distribution

Logarithmic general error distribution is an extension of lognormal distribution. In this paper, with optimal norming constants the higher-order expansion of distribution of partial maximum of logarithmic general error distribution is derived.

The General Characteristics and Distribution of the Glaucophane-Schist Belts of China

On the basis of the temperature variation, the glaucophane-schist facies Gan be classified into two faciesgroups, the glaucophane-lawsonite facies group and the glaucophane-greenschist facies group, and forms vari-ous facies series with other metamorphic facies. Glaucophane-schist belts of China are of different types withregard to their average T-P gradients and tectonic environments. They are: (1) Proterozoic intracratonicglaucophane-schist belts, (2) Caledonian intracratonic glaucophane-schist belts, (3) Palaeozoic pericratonicglaucophane-schist belts along the northern margin of the Chinese Platform, and (4) Meso-Cenozoicglaucophane-schist belts related to subduction. The initiation and evolution of glaucophane-schist metamorphism are related to their tectonic environ-ments. Most glaucophane-schist belts of China were formed in sialic environments. First the crust began tobreak up and eventually oceanic crust was formed. It seems that a non-uniformitarian mechanism may be in-volved as this evolution is related to the change of the configuration of the heat flow within the crust.

Generalized Truncated Fréchet Generated Family Distributions and Their Applications

Understanding a phenomenon from observed data requires contextual and efficient statistical models.Such models are based on probability distributions having sufficiently flexible statistical properties to adapt to a maximum of situations.Modern examples include the distributions of the truncated Fréchet generated family.In this paper,we go even further by introducing a more general family,based on a truncated version of the generalized Fréchet distribution.This generalization involves a new shape parameter modulating to the extreme some central and dispersion parameters,as well as the skewness and weight of the tails.We also investigate the main functions of the new family,stress-strength parameter,diverse functional series expansions,incomplete moments,various entropy measures,theoretical and practical parameters estimation,bivariate extensions through the use of copulas,and the estimation of the model parameters.By considering a special member of the family having the Weibull distribution as the parent,we fit two data sets of interest,one about waiting times and the other about precipitation.Solid statistical criteria attest that the proposed model is superior over other extended Weibull models,including the one derived to the former truncated Fréchet generated family.

Efficient Process Monitoring Under General Weibull Distribution

Product testing is a key ingredient in maintaining the quality of a pro-duction process.The production process is considered an efficient process if it is capable of quick identification of faulty products.The items produced by any production process are usually packed and acceptance or rejection of the pack depends upon its conformity to some specified quality level.Generally,the specified quality level is based upon the number of defective items found in the inspected number of items.Such decisions are based upon some rules and usually acceptance of the pack is based upon a fewer number of defective items in the pack.Such questions can be answered by using acceptance sampling plans.The acceptance sampling plans assume the fact that the quality level of the item follows some probability distribution.The sampling plans based upon some classical probability distributions are available but often it happens that the quality behavior of the product does not follow a simple probability model and hence the available sampling plans fail.In this paper,we have developed acceptance sampling plans when the product life follows a general Weibull distribution.The sampling plans have been constructed by considering the crisp and fuzzy behavior of the acceptance probability.These sampling plans have been constructed by assuming an infinite lot size.It has been found that the number of items required for inspection decreases with an increase in some parameters.

Topp-Leone Odd Fréchet Generated Family of Distributions with Applications to COVID-19 Data Sets

Recent studies have pointed out the potential of the odd Fréchet family(or class)of continuous distributions in fitting data of all kinds.In this article,we propose an extension of this family through the so-called“Topp-Leone strategy”,aiming to improve its overall flexibility by adding a shape parameter.The main objective is to offer original distributions with modifiable properties,from which adaptive and pliant statistical models can be derived.For the new family,these aspects are illustrated by the means of comprehensive mathematical and numerical results.In particular,we emphasize a special distribution with three parameters based on the exponential distribution.The related model is shown to be skillful to the fitting of various lifetime data,more or less heterogeneous.Among all the possible applications,we consider two data sets of current interest,linked to the COVID-19 pandemic.They concern daily cases confirmed and recovered in Pakistan from March 24 to April 28,2020.As a result of our analyzes,the proposed model has the best fitting results in comparison to serious challengers,including the former odd Fréchet model.

The Cox-Aalen Models as Framework for Construction of Bivariate Probability Distributions, Universal Representation

Starting with the Aalen （1989） version of Cox （1972） ＇regression model＇ we show the method for construction of ＂any＂ joint survival function given marginal survival functions. Basically, however, we restrict ourselves to model positive stochastic dependences only with the general assumption that the underlying two marginal random variables are centered on the set of nonnegative real values. With only these assumptions we obtain nice general characterization of bivariate probability distributions that may play similar role as the copula methodology. Examples of reliability and biomedical applications are given.

Rates of convergence of powered order statistics from general error distribution

Let{Xn:n≥1}be a sequence of independent random variables with common general error distribution GED(v)with shape parameter v>0,and let Mn,r denote the r-th largest order statistics of X1,X2,...,Xn.With different normalizing constants the distributional expansions and the uniform convergence rates of normalized powered order statistics|Mn,r|p are established.An alternative method is presented to estimate the probability of the r-th extremes.Numerical analyses are provided to support the main results.

Further Study on a Virtual Age Repair Model

A new virtual age repair model with non-uniform aging speed is presented on the basis of Kijima classical virtual age repair models which can be viewed as of uniform aging nature.In this model are included three types,of perfect,of imperfect and of minimal,all having a non-uniform aging speed.Formulas of expected count of repair and length of working time of these three models are derived,and numerical examples are also given to illustrate and verify obtained theoretical indices.As an extended work,a sketchy model of maintenance time of the non-uniform aging virtual age repair model is discussed.Overall,the three models discussed in the paper,each with non-uniform aging speed,are expansions to existing virtual age repair models,relevant formulas given here are new results,and the systems introduced are without the lifetime distribution assumption,all of which may be expected to improve maintenance work.

Study of transversity GPDs from pseudoscalar mesons production at EIC of China

The exclusive η and π^(0)electroproduction is studied in the handbag approach based on the generalized parton distributions(GPDs)factorization.Predictions of π^(0)and η mesons are calculated for future electron-ion collider in China(EicC)energy ranges,using obtained cross sections we extract information on the transversity GPDs contributions to these processes.

Exclusive π^(0) production at EIC of China within handbag approach

Exclusive π^(0) electroproduction is analyzed within the handbag approach based on Generalized Parton Distribution(GPDs)factorization.We consider the leading-twist contribution together with the transversity effects.It is shown that the transversity GPDs H_(T) and E_(T) are essential in the description of the π^(0) cross section.Predictions for the future Electron-Ion Collider of China(EicC)energy range are provided.It is found that transversity dominanceσ_(T)>>σ_(L),observed at low energies,is valid up to the EicC energy range.

Disentangling the spin-parity of a resonance via the gold-plated decay mode

Searching for new resonances and finding out their properties is an essential part of any existing or future particle physics experiment. The nature of a new resonance is characterized by its spin, charge conjugation,parity, and its couplings with the existing particles of the Standard Model. If a new resonance is found in the four lepton final state produced via two intermediate Z bosons, the resonance could be a new heavy scalar or a Z boson or even a higher spin particle. In such cases a step by step methodology as enunciated in this paper can be followed to determine the spin, parity and the coupling to two Z bosons of the parent particles, in a fully model-independent way. In our approach we show how three uni-angular distributions and a few experimentally measurable observables can conclusively tell us about the spin, parity as well as the couplings of the new resonance to two Z bosons. We have performed a numerical analysis to validate our approach and showed how the uni-angular observables can be used to disentangle the spin parity as well as the coupling of the resonance.