Generalized Half Logistic Distribution Research Articles

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.

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

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.

Estimation and prediction in generalized half logistic lifetime model using hybrid censored data

PurposeThis article aims to develop procedures for estimation and prediction in case of Type-I hybrid censored samples drawn from a two-parameter generalized half-logistic distribution (GHLD).Design/methodology/approachThe GHLD is a versatile model which is useful in lifetime modelling. Also, hybrid censoring is a time and cost-effective censoring scheme which is widely used in the literature. The authors derive the maximum likelihood estimates, the maximum product of spacing estimates and Bayes estimates with squared error loss function for the unknown parameters, reliability function and stress-strength reliability. The Bayesian estimation is performed under an informative prior set-up using the “importance sampling technique”. Afterwards, we discuss the Bayesian prediction problem under one and two-sample frameworks and obtain the predictive estimates and intervals with corresponding average interval lengths. Applications of the developed theory are illustrated with the help of two real data sets.FindingsThe performances of these estimates and prediction methods are examined under Type-I hybrid censoring scheme with different combinations of sample sizes and time points using Monte Carlo simulation techniques. The simulation results show that the developed estimates are quite satisfactory. Bayes estimates and predictive intervals estimate the reliability characteristics efficiently.Originality/valueThe proposed methodology may be used to estimate future observations when the available data are Type-I hybrid censored. This study would help in estimating and predicting the mission time as well as stress-strength reliability when the data are censored.

Inference on the Beta Type I Generalized Half Logistic Distribution under Right-Censored Observation with Application to COVID-19

In real-life situations, censoring issues do arise due to the incompleteness of data. This article examined the inferences on right-censored beta type I generalized half logistic distribution. In this work, some statistical properties of the beta type I generalized half logistic distribution were derived. Furthermore, the beta type I generalized half logistic distribution was studied under a censoring situation in the presence and absence of covariates. Estimation of model parameters was conducted using the maximum likelihood estimation method. A simulation study was carried out to assess the performance of the parameters of the model in terms of efficiency and consistency. In a real-life application, the model was applied to COVID-19 data and the necessary inferences were drawn.

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

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

Inference on the Beta Type I Generalized Half Logistic Distribution Under Right Censored Observation with Application to Covid-19

Inference on the Beta Type I Generalized Half Logistic Distribution Under Right Censored Observation with Application to Covid-19

Group Acceptance Sampling Plans for Resubmitted Lots UnderType II Generalized Half Logistic Distribution

In this research article, we build-up a group acceptance sampling plan (GASP) for a resubmitting lot when the lifetime of a product follow the Type II Generalized half-logistic distribution (GHLD). The design parameters of the group acceptance sampling plan for the resubmitted are determined by fixing the experiment termination time and the numbers of testers at the stated producer’s and consumer’s risks both satisfy at the same time. We contrast the proposed GASP with the ordinary group sampling plan and the results are demonstrated with a live data set.

Some Properties and Estimation of Parameters for the Five Parameter Type I Generalized Half Logistic Distribution under Complete Observation

This paper is a further study of the five parameter type I generalized half logistic distribution. We derived some properties of the distribution. Estimation of the parameters of the distribution under complete observation was studied using the maximum likelihood method. To assess the flexibility of the distribution, it was applied to a real lifetime data and the results when compared to the sub-models showed that the five parameter type I generalized half logistic distribution performed best.

The Beta Type I Generalized Half Logistic Distribution: Properties and Application

In a view to obtain a new distribution that is more exible than the type I generalized half logistic distribution, we used the beta-G generator and the type I generalized half logistic distribution. Some properties of the new distribution including the cummulative distribution function,survival function, hazard function were studied. Estimation of parameters were done using the maximum likelihood estimation method. Application of the derived distribution to lifetime data was illustrated by applying to remission times of bladder cancer patient data and survival times of guinea pigs.

A New Extension of the Generalized Half Logistic Distribution with Applications to Real Data.

In this paper, we introduced a new three-parameter probability model called Poisson generalized half logistic (PoiGHL). The new model possesses an increasing, decreasing, unimodal and bathtub failure rates depending on the parameters. The relationship of PoiGHL with the exponentiated Weibull Poisson (EWP), Poisson exponentiated Erlang-truncated exponential (PEETE), and Poisson generalized Gompertz (PGG) model is discussed. We also characterized the PoiGHL sub model, i.e the half logistic Poisson (HLP), based on certain functions of a random variable by truncated moments. Several mathematical and statistical properties of the PoiGHL are investigated such as moments, mean deviations, Bonferroni and Lorenz curves, order statistics, Shannon and Renyi entropy, Kullback-Leibler divergence, moments of residual life, and probability weighted moments. Estimation of the model parameters was achieved by maximum likelihood technique and assessed by simulation studies. The stress-strength analysis was discussed in detail based on maximum likelihood estimation (MLE), we derived the asymptotic confidence interval of based on the MLEs, and examine by simulation studies. In three applications to real data set PoiGHL provided better fit and outperform some other popular distributions. In the stress-strength parameter estimation PoiGHL model illustrated as a reliable choice in reliability analysis as shown using two real data set.

On the Flexibility of a Transmuted Type I Generalized Half Logistic Distribution with Application

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.

Stress–strength reliability analysis of multi-state system based on generalized survival signature

The stress–strength model has been widely used in reliability design of system. In the traditional stress–strength reliability theory, the system and each component are assumed to be only in one of two possible states being either working or failed, and the notion of stress–strength reliability is the probability that the strength is larger than the stress. In this paper, we study the stress–strength reliability of multi-state system based on generalized survival signature. It is supposed that the state of multi-state system is defined by using the ratio between strength and stress random variables. The definitions of generalized survival signature for a certain class of multi state systems with multi-state components in both discrete and continuous cases are given. In addition, the expressions of stress–strength reliability in both discrete and continuous situations are derived. In the case of continuous multi-state system, it is assumed that the random strength and stress are both from the Weibull distributions with different scale parameters, and the two different continuous kernel functions are Pareto and generalized half logistic distribution functions, respectively. Based on the assumptions, the stress–strength reliability is estimated by using both classical and Bayesian statistical theories. The uniformly minimum variance unbiased estimator and maximum likelihood estimator for the stress–strength reliability of the continuous multi-state system are derived. Under the squared error loss function, the exact expression of Bayes estimator for the stress–strength reliability of the continuous multi-state system is developed by using Gauss hypergeometric function. Finally, the Monte Carlo simulations are performed to compare the performances of the proposed stress–strength reliability estimators, and a real data set is also analyzed for an illustration of the findings. • The definitions of the generalized survival signature (GSS) are given. • We study the stress–strength reliability (SSR) of multi-state system based on GSS. • The multi-state system in both discrete and continuous cases are considered. • Classical and Bayesian statistical theories are used to estimate the SSR.

Bayesian and Non Bayesian Approach for the Estimations of Coefficient of Variation of Generalized Half Logistic Distribution Based on Type-I Censoring Samples

Bayesian and Non Bayesian Approach for the Estimations of Coefficient of Variation of Generalized Half Logistic Distribution Based on Type-I Censoring Samples

Estimation of P(X

PurposeThe purpose of this paper is to compare various methods of estimation of P(X<Y) based on Type-II censored data, where X and Y represent a quality characteristic of interest for two groups.Design/methodology/approachThis paper assumes that both X and Y are independently distributed generalized half logistic random variables. The maximum likelihood estimator and the uniformly minimum variance unbiased estimator of R are obtained based on Type-II censored data. An exact 95 percent maximum likelihood estimate-based confidence interval for R is also provided. Next, various Bayesian point and interval estimators are obtained using both the subjective and non-informative priors. A real life data set is analyzed for illustration.FindingsThe performance of various point and interval estimators is judged through a detailed simulation study. The finite sample properties of the estimators are found to be satisfactory. It is observed that the posterior mean marginally outperform other estimators with respect to the mean squared error even under the non-informative prior.Originality/valueThe proposed methodology can be used for comparing two groups with respect to a suitable quality characteristic of interest. It can also be applied for estimation of the stress-strength reliability, which is of particular interest to the reliability engineers.

Robust Bayesian Analysis of Generalized Half Logistic Distribution

In this paper, Robust Bayesian analysis of the generalized half logistic distribution (GHLD) under an $\epsilon$-contamination class of priors for the shape parameter $\lambda$ is considered. ML-II Bayes estimators of the parameters, reliability function and hazard function are derived under the squared-error loss function (SELF) and linear exponential (LINEX) loss function by considering the Type~II censoring and the sampling scheme of Bartholomew (1963). Both the cases when scale parameter is known and unknown is considered under Type~II censoring and under the sampling scheme of Bartholomew. Simulation study and analysis of a real data set are presented.

A Study of Five Parameter Type I Generalized Half Logistic Distribution

In this paper, we obtained a generalized half logistic distribution which is called a five-parameter type I generalized half logistic distribution. The distributional properties of the model such as the cumulative distribution function (cdf), moment, skewness, kurtosis, the median and the mode of the generalized distribution were established and finally a theorem that relate the distribution to pareto distribution was stated and proved.

Estimation and testing procedures for the reliability functions of generalized half logistic distribution

Two measures of reliability are considered, R(t)=P(X>t) and P=P(X>Y). Estimation and testing procedures are developed for R(t) and P under Type II cesoring and a sampling scheme of Bartholomew (1963). Two types of point estimators are considered (i) uniformly minimum variance unbiased estimators (UMVUEs) and (ii) maximum likelihood estimators (MLEs). A new technique of obtaining these estimators is introduced. A comparative study of different methods of estimation is done. Testing procedures are developed for the hypotheses related to different parametric functions.

The extended generalized half logistic distribution based on ordered random variables

In this paper, we considered an extended generalized half logistic distribution and derived some explicit expressions and recurrence relations for marginal and joint moment generating functions of generalized order statistics from extended generalized half logistic distribution. The results for record values and order statistics are deduced from the result. Finally, we obtained the characterizing result of this distribution on using the conditional expectation of generalized order statistics.

Bayes And Empirical Bayes Estimators based on Generalized Half Logistic Records Data

This study considers the estimation problem for the parameter and reliability function of Generalized Half logistic distribution under record Data. We use the maximum likelihood and Bayesian procedures to obtain the estimators of parameter and reliability function of Generalized Half logistic distribution. We also obtain the Empirical Bayesian Estimators for the parameter and reliability function of Generalized Half logistic distribution and considered the problem of predicting future record in a Bayesian and Empirical Bayesian approaches. Comparisons are made between the different estimators based on a simulation study.