Exact prediction intervals for future current records and record range from any continuous distribution

In this paper, a general method for predicting future lower and upper current records and record range from any arbitrary continuous distribution is proposed. Two pivotal statistics with the same explicit distribution for lower and upper current records are developed to construct prediction intervals for future current records. In addition, prediction intervals for future observations of the record range are constructed. A simulation study is applied on normal and Weibull distributions to investigate the efficiency of the suggested method. Finally, an example for real lifetime data with unknown distribution is analysed

A new least squares method for estimation and prediction based on the cumulative Hazard function

In this paper, the cumulative hazard function is used to solve estimation and prediction problems for generalized ordered statistics (defined in a general setup) based on any continuous distribution. The suggested method makes use of Rényi representation. The method can be used with type Ⅱ right-censored data as well as complete data. Extensive simulation experiments are implemented to assess the efficiency of the proposed procedures. Some comparisons with the maximum likelihood (ML) and ordinary weighted least squares (WLS) methods are performed. The comparisons are based on both the root mean squared error (RMSE) and Pitman's measure of closeness (PMC). Finally, two real data sets are considered to investigate the applicability of the presented methods

More Efficient Prediction for Ordinary Kriging to Solve a Problem in the Structure of Some Random Fields

Recently, some specific random fields have been defined based on multivariate distributions. This paper will show that almost all these random fields have a deficiency in spatial autocorrelation structure. The paper recommends a method for coping with this problem. Another application of these random fields is spatial data prediction, and the Kriging estimator is the most widely used method that does not require defining the mentioned random fields. Although it is an unbiased estimator with a minimum mean-squared error, it does not necessarily have a minimum mean-squared error in the class of all linear estimators. In this work, a biased estimator is introduced with less mean-squared error than the Kriging estimator under some conditions. Asymptotic behavior of its basic component will be investigated too

On estimation of P(Y < X) for inverse Pareto distribution based on progressively first failure censored data.

The stress-strength reliability (SSR) model ϕ = P(Y < X) is used in numerous disciplines like reliability engineering, quality control, medical studies, and many more to assess the strength and stresses of the systems. Here, we assume X and Y both are independent random variables of progressively first failure censored (PFFC) data following inverse Pareto distribution (IPD) as stress and strength, respectively. This article deals with the estimation of SSR from both classical and Bayesian paradigms. In the case of a classical point of view, the SSR is computed using two estimation methods: maximum product spacing (MPS) and maximum likelihood (ML) estimators. Also, derived interval estimates of SSR based on ML estimate. The Bayes estimate of SSR is computed using the Markov chain Monte Carlo (MCMC) approximation procedure with a squared error loss function (SELF) based on gamma informative priors for the Bayesian paradigm. To demonstrate the relevance of the different estimates and the censoring schemes, an extensive simulation study and two pairs of real-data applications are discussed

A New Model of Discrete-Continuous Bivariate Distribution with Applications to Medical Data

The bivariate Poisson exponential-exponential distribution is an important lifetime distribution in medical data analysis. In this article, the conditionals, probability mass function (pmf), Poisson exponential and probability density function (pdf), and exponential distribution are used for creating bivariate distribution which is called bivariate Poisson exponential-exponential conditional (BPEEC) distribution. Some properties of the BPEEC model are obtained such as the normalized constant, conditional densities, regression functions, and product moment. Moreover, the maximum likelihood and pseudolikelihood methods are used to estimate the BPEEC parameters based on complete data. Finally, two data sets of real bivariate data are analyzed to compare the methods of estimation. In addition, a comparison between the BPEEC model with the bivariate exponential conditionals (BEC) and bivariate Poisson exponential conditionals (BPEC) is considered

Residual and Past Discrete Tsallis and Renyi Extropy with an Application to Softmax Function

In this paper, based on the discrete lifetime distribution, the residual and past of the Tsallis and Renyi extropy are introduced as new measures of information. Moreover, some of their properties and their relation to other measures are discussed. Furthermore, an example of a uniform distribution of the obtained models is given. Moreover, the softmax function can be used as a discrete probability distribution function with a unity sum. Thus, applying those measures to the softmax function for simulated and real data is demonstrated. Besides, for real data, the softmax data are fit to a convenient ARIMA model

A novel logarithmic approach to generate new probability distributions for data modeling in the engineering sector

In this paper, we introduce a new statistical methodology for updating the flexibility level of the traditional distributions. The newly developed method is called, the logarithmic-U family of distributions. For the logarithmic-U distributions, the estimation of the parameters via the maximum likelihood method is discussed. Some mathematical properties of the logarithmic-U distributions are also derived. By using the logarithmic-U method, an updated version of the Weibull model, namely, the logarithmic Weibull distribution is introduced. A simulation study for the logarithmic Weibull distribution is provided. Finally, the practical illustration of the logarithmic Weibull distribution is shown by analyzing two data sets taken from the engineering sector. The first data set represents the fracture toughness of Al2O3 material. Whereas, the second data set represents the fatigue fracture of Kelvar 373/epoxy. The practical applications show that the proposed logarithmic Weibull distribution is very competent for analyzing data sets in engineering and other related sectors

A new improved form of the Lomax model: Its bivariate extension and an application in the financial sector

The Lomax model, also known as Pareto Type-II, has broad feasibility, especially in financing. This work introduces a new generalization of the Lomax model called the arc-sine exponentiation Lomax, which helps consider economic phenomena. The arc-sine exponentiation Lomax distribution captures a variety of shapes of density and hazard functions. The estimators of the proposed model’s parameters are derived using the maximum likelihood method. In a simulation study, the accuracy and efficacy of estimators are evaluated by computing their mean square errors and biases.Furthermore, a bivariate extension of the arc-sine exponentiation Lomax model is also introduced. The bivariate extension is introduced using Farlie–Gumble–Morgenstern copula approach. The new bivariate model is called Farlie–Gumble–Morgenstern arc-sine exponentiation Lomax distribution. Finally, a data set of thirty-two observations representing the export of goods demonstrates the arc-sine exponentiation Lomax model. The best-fitting results of the arc-sine exponentiatial Lomax are compared with some prominent extensions of the Lomax distribution

Visual illustration of the survival times data.

Statistical methodologies have a wider range of practical applications in every applied sector including education, reliability, management, hydrology, and healthcare sciences. Among the mentioned sectors, the implementation of statistical models in health sectors is very crucial. In the recent era, researchers have shown a deep interest in using the trigonometric function to develop new statistical methodologies. In this article, we propose a new statistical methodology using the trigonometric function, namely, a new trigonometric sine-G family of distribution. A subcase (special member) of the new trigonometric sine-G method called a new trigonometric sine-Weibull distribution is studied. The estimators of the new trigonometric sine-Weibull distribution are derived. A simulation study of the new trigonometric sine-Weibull distribution is also provided. The applicability of the new trigonometric sine-Weibull distribution is shown by considering a data set taken from the biomedical sector. Furthermore, we introduce an attribute control chart for the lifetime of an entity that follows the new trigonometric sine-Weibull distribution in terms of the number of failure items before a fixed time period is investigated. The performance of the suggested chart is investigated using the average run length. A comparative study and real example are given for the proposed control chart. Based on our study of the existing literature, we did not find any published work on the development of a control chart using new probability distributions that are developed based on the trigonometric function. This surprising gap is a key and interesting motivation of this research.</div

S1 Appendix -

Statistical methodologies have a wider range of practical applications in every applied sector including education, reliability, management, hydrology, and healthcare sciences. Among the mentioned sectors, the implementation of statistical models in health sectors is very crucial. In the recent era, researchers have shown a deep interest in using the trigonometric function to develop new statistical methodologies. In this article, we propose a new statistical methodology using the trigonometric function, namely, a new trigonometric sine-G family of distribution. A subcase (special member) of the new trigonometric sine-G method called a new trigonometric sine-Weibull distribution is studied. The estimators of the new trigonometric sine-Weibull distribution are derived. A simulation study of the new trigonometric sine-Weibull distribution is also provided. The applicability of the new trigonometric sine-Weibull distribution is shown by considering a data set taken from the biomedical sector. Furthermore, we introduce an attribute control chart for the lifetime of an entity that follows the new trigonometric sine-Weibull distribution in terms of the number of failure items before a fixed time period is investigated. The performance of the suggested chart is investigated using the average run length. A comparative study and real example are given for the proposed control chart. Based on our study of the existing literature, we did not find any published work on the development of a control chart using new probability distributions that are developed based on the trigonometric function. This surprising gap is a key and interesting motivation of this research.</div