Half Logistic Distribution Research Articles

Reliability Estimation of Scale Parameter in Type II Generalized Half-Logistic Distribution from Doubly Censored Samples Based on Monte Carlo Simulation

Objectives: This article deals with estimation of the reliability function for one-parameter Type II Generalized Half- Logistic distribution (Type II GHLD). Methods: The Maximum likelihood (ML) and Approximate Maximum likelihood (AML) methods provided by Jilani et.al. 1 . Findings: Comparisons between the estimators were made using Monte Carlo Simulation based on statistical indicter bias and mean squared error (MSE). We have generated 3000 random samples of size n=10(5)20 from a standard one-parameter Type II GHLD with = 0.5, 1.5 and 2.0. Each sample is then ordered and from this sample a doubly (including left and right) censored sample is considered, by censoring r smallest observations and s largest observations with all possible choices of r and s corresponding to this resultant sample we compute MLEs (using Newton-Raphson method), the LAMLE and unbiased LAMLE . Finally, the results are explained with tables. Novelty: This study has empirically proves that all the three reliability estimators have the same asymptotic variance. Hence, in this case, any one of the three estimators can be used but preferable estimator based unbiased estimator. Keywords: Maximum likelihood estimation, Approximate Maximum likelihood estimation, Bias, Mean squared error, Variances

Economic Design of Generalized Multiple Dependent State Sampling Plan Under Exponentiated Half Logistic Distribution

The main objective of this study is to propose an economic design of a generalized multiple dependent state sampling plan based on time truncated life test under exponentiated half logistic distribution for assuring median life. In this study, the optimal plan parameters are determined for various median ratios using the approach of two points on the operating characteristic curve. The performance of the proposed plan is compared with other sampling plans designed under exponentiated half logistic distribution. An investigation on the effect of misspecification of shape parameters on probabilities of lot acceptance is done and the industrial application of the proposed plan is explained with real time data. The results obtained from both conventional as well as economic designing show that the proposed plan outperforms the other existing sampling plans, such as multiple dependent state sampling plan, multiple dependent state repetitive group sampling plan, and single sampling plan.

Assessing the Bridge Structure’s System Reliability Utilizing the Generalized Unit Half Logistic Geometric Distribution

Reliability is now widely recognized across various industries, including manufacturing. This study investigates a system composed of five components, one of which is a bridge network. The components are assumed to follow the generalized unit half logistic geometric distribution (GUHLGD) with equal failure rates over time. The following three improvement methods are considered: reduction, cold duplication, and hot duplication. The reliability function and mean time to failure (MTTF) are employers liability equivalence factors (REFs). Additionally, the λ fractiles of both the original and enhanced systems are obtained. Numerical results illustrate the effectiveness of these techniques, with cold duplication shown to be the most effective, offering higher reliability and MTTF compared to hot duplication. The enhanced system outperforms the original system overall.

Exploring the Potential of the Kumaraswamy Discrete Half-Logistic Distribution in Data Science Scanning and Decision-Making

Exploring the Potential of the Kumaraswamy Discrete Half-Logistic Distribution in Data Science Scanning and Decision-Making

Different estimation techniques and data analysis for constant-partially accelerated life tests for power half-logistic distribution

Partial accelerated life tests (PALTs) are employed when the results of accelerated life testing cannot be extended to usage circumstances. This work discusses the challenge of different estimating strategies in constant PALT with complete data. The lifetime distribution of the test item is assumed to follow the power half-logistic distribution. Several classical and Bayesian estimation techniques are presented to estimate the distribution parameters and the acceleration factor of the power half-logistic distribution. These techniques include Anderson–Darling, maximum likelihood, Cramér von-Mises, ordinary least squares, weighted least squares, maximum product of spacing and Bayesian. Additionally, the Bayesian credible intervals and approximate confidence intervals are constructed. A simulation study is provided to compare the outcomes of various estimation methods that have been provided based on mean squared error, absolute average bias, length of intervals, and coverage probabilities. This study shows that the maximum product of spacing estimation is the most effective strategy among the options in most circumstances when adopting the minimum values for MSE and average bias. In the majority of situations, Bayesian method outperforms other methods when taking into account both MSE and average bias values. When comparing approximation confidence intervals to Bayesian credible intervals, the latter have a higher coverage probability and smaller average length. Two authentic data sets are examined for illustrative purposes. Examining the two real data sets shows that the value methods are workable and applicable to certain engineering-related problems.

Epidemiological modeling of COVID-19 data with Advanced statistical inference based on Type-II progressive censoring

This research proposes the Kavya-Manoharan Unit Exponentiated Half Logistic (KM-UEHL) distribution as a novel tool for epidemiological modeling of COVID-19 data. Specifically designed to analyze data constrained to the unit interval, the KM-UEHL distribution builds upon the unit exponentiated half logistic model, making it suitable for various data from COVID-19. The paper emphasizes the KM-UEHL distribution's adaptability by examining its density and hazard rate functions. Its effectiveness is demonstrated in handling the diverse nature of COVID-19 data through these functions. Key characteristics like moments, quantile functions, stress-strength reliability, and entropy measures are also comprehensively investigated. Furthermore, the KM-UEHL distribution is employed for forecasting future COVID-19 data under a progressive Type-II censoring scheme, which acknowledges the time-dependent nature of data collection during outbreaks. The paper presents various methods for constructing prediction intervals for future-order statistics, including maximum likelihood estimation, Bayesian inference (both point and interval estimates), and upper-order statistics approaches. The Metropolis-Hastings and Gibbs sampling procedures are combined to create the Markov chain Monte Carlo simulations because it is mathematically difficult to acquire closed-form solutions for the posterior density function in the Bayesian framework. The theoretical developments are validated with numerical simulations, and the practical applicability of the KM-UEHL distribution is showcased using real-world COVID-19 datasets.

Development and validation of accelerated failure time model for cause-specific survival and prognostication of oral squamous cell carcinoma: SEER data analysis.

Oral Squamous Cell Carcinoma is the most prevalent malignancies affecting the oral cavity. Despite progress in studies and treatment options its outlook remains grim with survival prospects greatly affected by demographic and clinical factors. Precisely predicting survival rates and prognosis plays a role in making treatment choices for the best achievable overall health outcomes. To develop and validate an accelerated failure time model as a predictive model for cause-specific survival and prognosis of Oral Squamous Cell Carcinoma patients and compare its results to the traditional Cox proportional hazard model. We screened Oral cancer patients diagnosed with Squamous Cell Carcinoma from the Surveillance Epidemiology and End Results (SEER) database between 2010 and 2020. An accelerated failure time model using the Type I generalized half logistic distribution was used to determine independent prognostic factors affecting the survival time of patients with oral squamous carcinoma. In addition, accelerated factors were estimated to assess how some variables influence the survival times of the patients. We used the Akaike Information Criterion, Bayesian Information Criterion to evaluate the model fit, the area under the curve for discriminability, Concordance Index (C-index) and Root Mean Square Error and calibration curve for predictability, to compare the type I generalized half logistic survival model to other common classical survival models. All tests are conducted at a 0.05 level of significance. The accelerated failure time models demonstrated superior effectiveness in modeling (fit and predictive accuracy) the cause-specific survival (CSS) of oral squamous cell carcinoma compared to the Cox model. Among the accelerated failure time models considered, the Type I generalized half logistic distribution exhibited the most robust model fit, as evidenced by the lowest Akaike Information Criterion (AIC = 27370) and Bayesian Information Criterion (BIC = 27415) values. This outperformed other parametric models and the Cox Model (AIC = 47019, BIC = 47177). The TIGHLD displayed an AUC of 0.642 for discrimination, surpassing the Cox model (AUC = 0.544). In terms of predictive accuracy, the model achieved the highest concordance index (C-index = 0.780) and the lowest root mean square error (RMSE = 1.209), a notable performance over the Cox model (C-index = 0.336, RMSE = 6.482). All variables under consideration in this study demonstrated significance at the 0.05 level for CSS, except for race and the time span from diagnosis to treatment, in the TIGHLD AFT model. However, differences emerged regarding the significant variations in survival times among subgroups. Finally, the results derived from the model revealed that all significant variables except chemotherapy, all TNM stages and patients with Grade II and III tumor presentations contributed to the deceleration of time to cause-specific deaths. The accelerated failure time model provides a relatively accurate method to predict the prognosis of oral squamous cell carcinoma patients and is recommended over the Cox PH model for its superior predictive capabilities. This study also underscores the importance of using advanced statistical models to improve survival predictions and outcomes for cancer patients.

A novel flexible T-X family for generating new distributions with applications to lifetime data

In recent decades, many research studies have been conducted for the development of some new modifications of different baseline distributions to cope with real-world problems. This paper proposes a novel generalization of probability distributions, called modified type- II half-logistic distribution. We have derived the new family of probability distributions using T-X family with input as a type II variant of the half-logistic distribution. For the purpose of demonstration, the Weibull distribution is considered as a sub-model. Various algebraic properties of the suggested distribution have been discussed. For efficient parameter estimation, we have used the maximum likelihood principle. Additionally, two real-world data sets from the literature have been considered to illustrate the practical usefulness and significance of the suggested model.

Inferences on stress-strength reliability $$R=\text{ P }[Y<X<Z]$$ for progressively type-II censored Weibull half logistic distribution

Inferences on stress-strength reliability $$R=\text{ P }[Y<X<Z]$$ for progressively type-II censored Weibull half logistic distribution

On the Type I Half Logistic Lomax Distribution with applications

On the Type I Half Logistic Lomax Distribution with applications

Monitoring the inverted exponentiated half logistic quantiles under the adaptive progressive type II hybrid censoring scheme

Numerous studies have solved the problem of monitoring statistical processes with complete samples. However, censored or incomplete samples are commonly encountered due to constraints such as time and cost. Adaptive progressive Type II hybrid censoring is a novel method with the advantages of saving time and improving efficiency. On the basis of this scheme, the problem of monitoring a downward shift in the quantiles of the inverted exponentiated half logistic distribution is considered. The conventional Shewhart control chart is insensitive to detect quantile shifts from faulty data processes that exhibit deviations from normality or symmetry. To overcome this limitation, Bootstrap control charts combining with the exponentially weighted moving average method based on the Bayesian estimation and maximum likelihood estimation are proposed, respectively. They are compared with the conventional Shewhart control chart via average run length through Monte-Carlo simulations. Finally, a real dataset related to the tensile strength of carbon fibers is employed to demonstrate the ascendancy of the Bootstrap control charts.

A Discrete Version of the Half-Logistic Distribution Based on the Mimicking of the Probability Density Function

We introduce a count distribution obtained as a discrete analogue of the continuous half-logistic distribution. It is derived by assigning to each non-negative integer value a probability proportional to the corresponding value of the density function of the parent model. The main features of this new distribution, in particular related to its shape, moments, and reliability properties, are described. Parameter estimation, which can be carried out resorting to different methods including maximum likelihood, is discussed, and a numerical comparison of their performances, based on Monte Carlo simulations, is presented. The applicability of the proposed distribution is proved on two real datasets, which have been already fitted by other well-established count distributions. In order to increase the flexibility of this counting model, a generalization is finally suggested, which is obtained by adding a shape parameter to the continuous one-parameter half-logistic and then applying the same discretization technique, based on the mimicking of the density function.

Designing of multiple dependent state sampling plan for Type-II generalized half logistic distribution

Designing of multiple dependent state sampling plan for Type-II generalized half logistic distribution

A novel extension of half-logistic distribution with statistical inference, estimation and applications

In the present study, we develop and investigate the odd Frechet Half-Logistic (OFHL) distribution that was developed by incorporating the half-logistic and odd Frechet-G family. The OFHL model has very adaptable probability functions: decreasing, increasing, bathtub and inverted U shapes are shown for the hazard rate functions, illustrating the model’s capacity for flexibility. A comprehensive account of the mathematical and statistical properties of the proposed model is presented. In estimation viewpoint, six distinct estimation methodologies are used to estimate the unknown parameters of the OFHL model. Furthermore, an extensive Monte Carlo simulation analysis is used to evaluate the effectiveness of these estimators. Finally, two applications to real data are used to demonstrate the versatility of the suggested method, and the comparison is made with the half-logistic and some of its well-known extensions. The actual implementation shows that the suggested model performs better than competing models.

A Discrete Odd Lindley Half-Logistic Distribution with Applications

In the reality, the most of lifetime data is discrete in nature, despite it is known that this data is continuous. As a consequence, the tendency to convert the continuous lifetime distributions to its discrete counterpart has raised. The nature of the most lifetime data in real life is discrete, thus, many of researchers interested to convert. This article aims to introduce a new one-parameter discrete distribution, namely Discrete Odd Lindley Half-Logistic (DOLiHL) distribution. The DOLiHL distribution is derived by discretizing the analogue continuous distribution, using a survival discretization technique. An intensive study of this distribution is provided, including characteristic functions and statistical properties. Moreover, the unknown parameter is estimated using different methods of estimation namely, the maximum likelihood method, method of moments, least squares method and Cramer-von Mises minimum distance estimation method. A simulation study is conducted to examine the distribution’s behavior and compare between the estimation methods at different sample sizes. To evaluate the efficiency of this distribution against other competitive distributions, an implementation on real data in different fields is performed. In conclude, the DOLiHL distribution has assured its efficiency of fitting in lifetime and count data from various fields in real life.

Discrete half-logistic distributions with applications in reliability and risk analysis

In the statistical literature, several discrete distributions have been developed so far for modeling non-negative integer-valued phenomena, yet there is still room for new counting models that adequately capture the diversity of real data sets. Here, we first discuss a count distribution derived as a discrete analogue of the continuous half-logistic distribution, which is obtained by preserving the expression of its survival function at each non-negative integer support point. The proposed discrete distribution has a mode at zero and allows for over-dispersion; these two features make it suitable for modeling purposes in many fields (e.g., insurance and ecology), when these conditions are satisfied by the data. In order to widen its spectrum of applications, a discrete analogue is also presented of the type I generalized half-logistic distribution (obtained by adding a shape parameter to the simple one-parameter half-logistic), which allows us to model count data whose mode is not necessarily zero. For these new count distributions, the main statistical properties are outlined, and parameter estimation along with related issues is discussed. Their feasibility is proved on two real data sets taken from the literature, which have already been fitted by other well-established count distributions. Finally, a possible application is illustrated in the insurance field, related to the exact/approximate determination of the distribution of the total claims amount through the well-known Panjer’s recursive formula, within the framework of collective risk models.

An Alternative Discrete Analogue of the Half-Logistic Distribution Based on Minimization of a Distance between Cumulative Distribution Functions

A discrete version of the continuous half-logistic distribution is introduced, which is based on the minimization of the Cramér distance between the corresponding continuous and step-wise cumulative distribution functions. The expression of the probability mass function is derived in an analytic form, and some properties of the distribution - mainly related to moments and reliability concepts - are discussed. As for sample estimation, three different techniques are suggested, whose theoretical and empirical features are examined also through a Monte Carlo simulation study, comprising several parameter and sample size combinations. A comparison is also made between the proposed distribution and a discrete version already proposed in the literature, based on a different rationale, and a main difference is highlighted. A count regression model is suggested where the response variable follows the discrete half-logistic distribution and artificial and real data are used to illustrate its use. Finally, the performance of the proposed distribution over other classical models is discussed based on a real data set.

Transformation of Rayleigh Distribution, Properties, and Application

The need to develop the theory of statistics and its properties follows from the fact that many types of data cannot be fitted by classical distributions. This fact invites many researchers to generate new distributions, find their properties, and implement a data set to find the best distribution that can fit the data better. In this paper, we propose special cases of Rayleigh distribution and their relationship to wellknown distributions like half-logistic distribution (HLD), generalized half-logistic distribution (GHLD), and exponentiated half-logistic distribution (EHLD). We have mainly discussed the relationship of a transformation technique of those special cases of Rayleigh distribution with different parameter values to the assigned distributions (HLD, GHLD, EHLD). We also show the mathematical statistical properties of such special cases like the rth moment, central moment, incomplete moments, the probability weighted moments, the stochastic ordering, and interval estimation within the proposed parameters. Consequently, such properties are derived to generate modern statistical characteristics related to the special cases of Rayleigh distribution. Moreover, we have set table for the calculations of particular cases with their derived moments that have previously found their theoretical representations. Finally, we set off some conclusions related to the results of this humble work.

Discrete Half-Logistic Distribution: Statistical Properties, Estimation, and Application

Discrete Half-Logistic Distribution: Statistical Properties, Estimation, and Application

Alpha Logarithm Transformed Half Logistic Distribution: Properties and Applications

Abstract: In this paper, we introduce a new two parameter Alpha Logarithm Transformed Half Logistic (ALTHL) distribution. A new method has been proposed to introduce an extra parameter to a family of distributions for more flexibility .The proposed family may be named as Alpha Logarithm Transformed Half Logistic. This can be obtained via reparameterizing the exponentiated Kumaraswamy G-logarithmic family and the alpha logarithmic family of distributions. The recommended distribution reveals increasing, decreasing and bath-shaped probability Density, Distribution and Hazard rate function and Survival function. Some distributional properties of new model are investigated which include the Density Function, Distribution Function (DF), Quantile Function(QF), Moments, Moment Generating Function (MGF), Cumulative Generating Function (CGF).