On the Type-I Half-logistic Distribution and Related Contributions: A Review

In this article we transmute the type I half logistic distribution using quadratic rank transmutation map to develop a transmuted type I half logistic distribution. The quadratic rank transmutation map enables the introduction of extra parameter into its baseline distribution to enhance more flexibility in the analysis of data in various disciplines such as reliability analysis in engineering, survival analysis, medicine, biological sciences, actuarial science, finance and insurance. The mathematical properties such as moments, quantile, mean, median, variance, skewness and kurtosis of this distribution are discussed. The reliability and hazard functions of the transmuted type I half logistic distribution are obtained. The probability density functions of the minimum and maximum order statistics of the transmuted type I half logistic distribution are established and the relationships between the probability density functions of the minimum and maximum order statistics of the parent model and the probability density function of the transmuted type I half logistic distribution are considered. The parameter estimation is done by the method of maximum likelihood estimation. The flexibility of the model in statistical data analysis and its applicability is demonstrated by using it to fit relevant data. The study is concluded by demonstrating that the transmuted type I half logistic distribution has a better goodness of fit than its parent model. We hope this model will serve as an alternative to the existing ones in the literature in fitting positive real data.

This paper develops maximum likelihood estimators (MLEs) of unknown param-eters in an exponentiated half-logistic distribution based on a progressively type-IIcensored sample. We obtain approximate con dence intervals for the MLEs by usingasymptotic variance and covariance matrices. Using importance sampling, we obtainBayes estimators and corresponding credible intervals with the highest posterior densityand Bayes predictive intervals for unknown parameters based on progressively type-IIcensored data from an exponentiated half logistic distribution. For illustration pur-poses, we examine the validity of the proposed estimation method by using real andsimulated data.Keywords: Bayes predictive interval, exponentiated half-logistic distribution, HPD cred-ible interval, importance sampling, progressively type-II censored sample. 1. Introduction Many reliability and survival analysis studies have used half-logistic distributions, partic-ularly for censored data. Several studies have drawn inferences about half logistic distribu-tions. Balakrishnan and Puthenpura (1986) introduce the best linear unbiased estimator oflocation and scale parameters of half-logistic distributions by considering linear functionsof order statistics. Balakrishnan and Wong (1991) obtain approximate maximum likelihoodestimators (AMLEs) of location and scale parameters of half-logistic distributions by usinga type-II right-censored sample. Kang et al. (2008) derive AMLEs and MLEs of scale pa-rameters of half-logistic distributions by using progressively type-II censored samples. Kanget al. (2009) propose AMLEs of scale parameters of half-logistic distributions by consideringdouble-hybrid censored samples. Kang and Seo (2011) recently examine exponentiated half-logistic distributions and propose two types of AMLEs of scale parameters and reliabilityfunctions by using progressively type-II right-censored samples. Kim et al. (2011a) deriveBayesian estimators of shape parameters, reliability functions, and failure rate functions

This book presents the theory of probability and mathematical statistics at a level suitable for researchers at the frontiers of applied disciplines. Examples and exercises make essential concepts in measure theory and analysis accessible to those with preparation limited to vector calculus. Complete, detailed solutions to all the exercises demonstrate techniques of problem solving and provide immediate feedback. Part I, The Theory of Probability, starts with elementary set theory and proceeds through basic measure and probability, random variables, integration and mathematical expectation. It concludes with an extensive survey of models for distributions of random variables. Part II, The Theory of Statistics, begins with sampling theory and distribution theory for statistics from normal populations, proceeds to asymptotic (large-sample) theory, and on to point and interval estimation and tests of parametric hypotheses. The last three chapters cover tests of nonparametric hypotheses, Bayesian methods, and linear and nonlinear regression. Researchers and graduate students in applied fields such as actuarial science, biostatistics, economics, finance, mathematical psychology, and systems engineering will find this book to be a valuable learning tool and an essential reference. Contents: The Theory of Probability: Probability on Abstract Sets Probability on Sets of Real Numbers Mathematical Expectation Models for Distributions The Theory of Statistics: Sampling Distributions Asymptotic Distribution Theory Estimation Tests of Parametric Hypotheses Tests of Nonparametric Hypotheses A Survey of Bayesian Methods Regression Analysis Readership: Researchers and graduate students in applied fields such as actuarial science, biostatistics, economics, finance, mathematical psychology, and systems engineering. Key Features: Present basic concepts in real and complex analysis and measure theory along with the applications to probability Difficult theoretical points are followed directly by examples and exercises with detailed solutions Provide a survey of Bayesian methods and an extensive treatment of goodness-of-fit tests Suitable learning tool for students and researchers in applied fields for whom a rigorous foundation in probability and statistical inference is essential

Some Thoughts About Data Type, Distribution, and Statistical Significance

This paper presents a novel extension of the exponentiated inverse Rayleigh distribution called the half-logistic exponentiated inverse Rayleigh distribution. This extension improves the flexibility of the distribution for modeling lifetime data for both monotonic and non-monotonic hazard rates. The statistical properties of the half-logistic exponentiated inverse Rayleigh distribution, such as the quantiles, moments, reliability, and hazard function, are examined. In particular, we provide several techniques to estimate the half-logistic exponentiated inverse Rayleigh distribution parameters: weighted least squares, Cramér-Von Mises, maximum likelihood, maximum product spacings and ordinary least squares methods. Moreover, numerical simulations were performed to evaluate these estimation methods for both small and large samples through Monte Carlo simulations, and the finding reveals that the maximum likelihood estimation was the best among all estimation methods since it comprises small mean square error compared to other estimation methods. We employ real-world lifetime data to demonstrate the performance of the newly generated distribution compared to other distributions through practical application. The results show that the half-logistic exponentiated inverse Rayleigh distribution performs better than alternative versions of the Rayleigh distributions.

Previous article Next article The Central Limit Theorem for a Sequence of Random Variables with a Slowly Growing Number of DependencesM. B. Petrovskaya and A. M. LeontovichM. B. Petrovskaya and A. M. Leontovichhttps://doi.org/10.1137/1127089PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] V. B. Ivanov, Cell Foundations of Plant Growth, Nauka, Moscow, 1974, (In Russian.) Google Scholar[2] Z. A. Lomnicki and , S. K. Zaremba, A further instance of the central limit theorem for dependent random variables, Math. Z, 66 (1957), 490–494 20:6152 0077.33101 CrossrefGoogle Scholar[3] A. F. Ronzhin, On limit theorems for sums of dependent random variables, Theory Prob. Appl., 24 (1979), 549–559 0435.60023 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails When Janson meets McDiarmid: Bounded difference inequalities under graph-dependenceStatistics & Probability Letters, Vol. 17 Cross Ref Weighted dependency graphsElectronic Journal of Probability, Vol. 23, No. none Cross Ref Dependency graphs and mod-Gaussian convergence7 December 2016 Cross Ref A law of large numbers for nearest neighbour statistics12 August 2008 | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 464, No. 2100 Cross Ref Central limit theorems for k-nearest neighbour distancesStochastic Processes and their Applications, Vol. 85, No. 2 Cross Ref On the variance of the random sphere of influence graphRandom Structures and Algorithms, Vol. 14, No. 2 Cross Ref On a Theorem of JansonV. G. Mikhailov17 July 2006 | Theory of Probability & Its Applications, Vol. 36, No. 1AbstractPDF (378 KB)Asymptotic normality of some Graph-Related statistics14 July 2016 | Journal of Applied Probability, Vol. 26, No. 1 Cross Ref On a Condition for Slowly Growing Number of DependenciesA. M. Leontovich28 July 2006 | Theory of Probability & Its Applications, Vol. 30, No. 1AbstractPDF (623 KB) Volume 27, Issue 4| 1983Theory of Probability & Its Applications History Submitted:20 December 1977Published online:17 July 2006 InformationCopyright © 1983 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1127089Article page range:pp. 815-825ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

The Half-Logistic (HL) distribution is a renowned lifetime distribution widely used in various domains, including reliability engineering, biological sciences, and actuarial research. Despite its fundamental simplicity and easy interpretation, the HL distribution has limitations in terms of flexibility for modeling datasets with heavy tails or varying skewness. To address these constraints, this paper introduces a new extension of the HL distribution based on the Odd Beta Prime (OBP) family. The newly developed distribution has two shape parameters and is named the Odd Beta Prime Half-Logistic (OBPHL) distribution. Its several distributional properties, including the probability density function, cumulative distribution function, survival function, hazard function, and quantile function, alongside other various distributional characteristics, such as moments, measures of skewness and kurtosis, entropy measure ( Rényi and Tsallis), and order statistics, are explored. The maximum likelihood estimation technique is used to estimate the parameters of the new model. The performance of the estimators under different sample sizes has been evaluated using a Monte Carlo simulation study. In addition, the proposed OBPHL distribution is applied to two real-world datasets. The results are compared against several classical distributions using standard model selection criteria. The OBPHL distribution consistently outperforms the competing models based on evaluation metrics. This research contributes a new flexible model to the field of statistical distribution theory and demonstrates its efficacy in practical applications.

Recent advances of information technology in biomedical sciences and other applied areas have created numerous large diverse data sets with a high dimensional feature space, which provide us a tremendous amount of information and new opportunities for improving the quality of human life. Meanwhile, great challenges are also created driven by the continuous arrival of new data that requires researchers to convert these raw data into scientific knowledge in order to benefit from it. Association studies of complex diseases using SNP data have become more and more popular in biomedical research in recent years. In this paper, we present a review of recent statistical advances and challenges for analyzing correlated high dimensional SNP data in genomic association studies for complex diseases. The review includes both general feature reduction approaches for high dimensional correlated data and more specific approaches for SNPs data, which include unsupervised haplotype mapping, tag SNP selection, and supervised SNPs selection using statistical testing/scoring, statistical modeling and machine learning methods with an emphasis on how to identify interacting loci.

Chapter 5 - Nanotechnology-based regenerative approaches

In this paper, we introduce a new three-parameter lifetime model called the extended half-logistic (EHL) distribution. We derive various of its structural properties including moments, quantile and generating functions, mixture representation for probability density function, and reliability curves. The maximum likelihood, ordinary and weighted least square methods are used to estimate the model parameters. Simulation results to assess the performance of the estimation methods are discussed. We conclude that the maximum likelihood is the most suitable method to estimate model parameters for the small sample size. While the weighted least square method is the best for the large sample size. Finally, we prove empirically the importance and flexibility of the new model in modeling a real lifetime dataset.

This article presents a case study to show the usefulness and importance of using factorial design in tissue engineering and biomaterials science. We used a full factorial experimental design (2 × 2 × 2 × 3) to solve a routine query in every biomaterial research project: the optimisation of cell seeding efficiency for pre-clinical in vitro cell studies, the importance of which is often overlooked. In addition, tissue-engineered scaffolds can be cellularised with relevant cell type(s) to form implantable tissue constructs, where the cell seeding method must be reliable and robust. Our results show the complex relationship between cells and scaffolds and suggest that the optimum seeding conditions for each material may be different due to different material properties, and therefore, should be investigated for individual scaffolds. Our factorial experimental design can be easily translated to other cell types and three-dimensional biomaterials, where multiple interacting variables can be thoroughly investigated for better understanding of cell–biomaterial interactions.

First, we discuss basic probability notions from the viewpoint of category theory. Our approach is based on the following four “sine quibus non” conditions: 1. (elementary) category theory is efficient (and suffices); 2. random variables, observables, probability measures, and states are morphisms; 3. classical probability theory and fuzzy probability theory in the sense of S. Gudder and S. Bugajski are special cases of a more general model; 4. a good model allows natural modifications. Second, we show that the category ID of D-posets of fuzzy sets and sequentially continuous D-homomorphisms allows to characterize the passage from classical to fuzzy events as the minimal generalization having nontrivial quantum character: a degenerated state can be transported to a nondegenerated one. Third, we describe a general model of probability theory based on the category ID so that the classical and fuzzy probability theories become special cases and the model allows natural modifications. Finally, we present a modification in which the closed unit interval [0,1] as the domain of traditional states is replaced by a suitable simplex.

We are entering an era of unprecedented opportunities and challenges in health and medicine. With recent advances in science and technology, as well as the advent of big data, we have seen tremendous developments in biomedical science and the practice of medicine. Yet, the global disease burden continues to rise, demand for care is increasing, costs are unsustainable, and health inequity persists. Globally, cardiovascular disease (CVD) is the No. 1 disease burden, driven by the rise in noncommunicable diseases such as obesity and diabetes mellitus. The need for cardiovascular medicine will continue to grow as the global population ages and developing countries become more affluent, adopt a Western lifestyle, and become more urbanized. There have been impressive advances in cardiovascular diagnostics and therapeutics in the areas of precision medicine, molecular/metabolic imaging, endovascular procedures, gene and cell therapies, RNA therapeutics, tissue engineering and regenerative medicine, and digital health. However, cardiovascular care is fragmented and expensive. Furthermore, in the current healthcare landscape, access, quality, and costs are top priorities. The Affordable Care Act introduced a number of payment and delivery system reforms to increase the quality of health care while controlling costs, such as accountable care organizations, patient-centered medical homes, and mechanisms to link payments to quality. This value-focused health care is here to stay; therefore, we must adopt this approach for cardiovascular medicine. Importantly, we must do more to move from a disease-treatment model to a model that prioritizes and enables prevention. Unfortunately, current health challenges do not always lend themselves to straightforward solutions. There is a real need for evidence-based, independent, and nonpolitical advice that can inform health policy and thereby shape solutions and drive change. Indeed, society can benefit enormously from the activities of an independent scientific academy with the directive to mobilize the best minds to provide objective …

Purpose. Increasing the efficiency of the conveyor transport system of the mine due to the application of rational parameters, which are calculated objectively on the basis of the reliable output data of random freight flow in the conveyor transport line, taking into account the velocity of minerals transportation, including a perfect theoretical model application of the freight flow distribution. Methodology. Complex research: - statistical studies on the actual distribution of random freight flow in the highly productive stages of the PSU Mine “n.a Heroiv Kosmosu” PJSC “DTEK Pavlohradvuhillia”; - description of histograms of the distribution of random freight flow by various indicative algebraic functions, normal and gamma distribution of a random variable and a specially constructed function with separately defined parameters of its branches; - analysis of research results regarding the correctness of the theoretical model of the distribution of random freight flow according to various criteria of genuineness, a center of grouping, amplitude, velocity of rise and fall, and deviation. Findings. A perfect theoretical model was built in the form of an indicative algebraic function, whose branches are described by the normal distribution law of a random variable with separately determined parameters. It describes well the distribution of random freight flow in the conveyor transport line of the mine and ensures the determination of its parameters by the methods of probability theory. Originality. A theoretical model of the distribution of random freight flow in the conveyor transport line of the mine has been obtained for the first time, which describes well various cases of its distribution, including symmetric and asymmetric ones, and provides the determination of the freight flow parameters by the methods of probability theory. Practical value. The actual value of the coefficient of nonuniformity of the freight flow in the conveyor transport line of the mine, which was determined by a perfect theoretical model, exceeds, by almost a quarter, the value inherent in the model accepted in practice, the normal law of the distribution of a random variable. The coefficient of nonuniformity of the freight flow in the highly productive longwalls of only the specified mine reaches a value of 2.012, which already exceeds the normative value limit for conveyor transport lines along horizontal and inclined preparatory workings of mining areas (2.0). Reliable initial data on the variation of the random freight flow in the conveyor transport line of the mine, which is substantiated by a perfect theoretical model of its distribution, have a positive effect on the calculation of its parameters and contribute to increasing the efficiency and reliability of the functioning of the conveyor transport system.

Chapter 19 - Computational biology and biosensors as surveillance tools for emerging and re-emerging infectious diseases