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In this article, a progressive Type II censoring plan with binomial removal is utilized to overcome the estimation issues associated with the truncated Cauchy power‐inverted Topp‐Leone distribution (TCPITLD). Using maximum likelihood and Bayesian estimation approaches is a means of estimating the unknown parameter. Bayesian estimators are studied using the likelihood function when observed data are produced. This is done by employing the assumption of an informative prior, a gamma prior, and a symmetric loss function. Both of these assumptions are made. In addition, the discussion also includes the approximate confidence intervals obtained by using both the classical technique and the credible intervals with the most significant posterior density. A detailed simulation experiment that considers a variety of sample sizes and censoring techniques is carried out to evaluate the various estimation procedures. A single actual dataset is investigated to validate the effectiveness of the TCPITLD and the estimators provided during the process. The findings indicate that the Bayesian strategy that uses the gamma prior is preferable to both the maximum likelihood technique and the Bayesian approach that uses the informative prior to acquiring the required estimators.

This paper aims to find a statistical model for the COVID-19 spread in the United Kingdom and Canada. We used an efficient and superior model for fitting the COVID 19 mortality rates in these countries by specifying an optimal statistical model. A new lifetime distribution with two-parameter is introduced by a combination of inverted Topp-Leone distribution and modified Kies family to produce the modified Kies inverted Topp-Leone (MKITL) distribution, which covers a lot of application that both the traditional inverted Topp-Leone and the modified Kies provide poor fitting for them. This new distribution has many valuable properties as simple linear representation, hazard rate function, and moment function. We made several methods of estimations as maximum likelihood estimation, least squares estimators, weighted least-squares estimators, maximum product spacing, Crame´r-von Mises estimators, and Anderson-Darling estimators methods are applied to estimate the unknown parameters of MKITL distribution. A numerical result of the Monte Carlo simulation is obtained to assess the use of estimation methods. also, we applied different data sets to the new distribution to assess its performance in modeling data.

This paper aims at defining an optimal statistical model for the COVID-19 distribution in the United Kingdom, and Canada. A combining the inverted Topp–Leone distribution and the odd Weibull family introduces a new lifetime distribution with a three-parameter to formulate the odd Weibull inverted Topp–Leone (OWITL) distribution. As a simple linear representation, hazard rate function, and moment function, this new distribution has several nice properties. To estimate the unknown parameters of OWITL distribution, maximum likelihood, least-square, weighted least-squares, maximum product spacing, Cramér–von Mises estimators, and Anderson–Darling estimation methods are used. To evaluate the use of estimation techniques, a numerical outcome of the Monte Carlo simulation is obtained.

The quadratic rank transmutation map is used in this article to suggest a novel extension of the power inverted Topp–Leone distribution. The newly generated distribution is known as the transmuted power inverted Topp–Leone (TPITL) distribution. The power inverted Topp–Leone and the inverted Topp–Leone are included in the recommended distribution as specific models. Aspects of the offered model, including the quantile function, moments and incomplete moments, stochastic ordering, and various uncertainty measures, are all discussed. Plans for acceptance sampling are created for the TPITL model with the assumption that the life test will end at a specific time. The median lifetime of the TPITL distribution with the chosen variables is the truncation time. The smallest sample size is required to obtain the stated life test under a certain consumer's risk. Five conventional estimation techniques, including maximum likelihood, least squares, weighted least squares, maximum product of spacing, and Cramer-von Mises, are used to assess the characteristics of TPITL distribution. A rigorous Monte Carlo simulation study is used to evaluate the effectiveness of these estimators. To determine how well the most recent model handled data modeling, we tested it on a range of datasets. The simulation results demonstrated that, in most cases, the maximum likelihood estimates had the smallest mean squared errors among all other estimates. In some cases, the Cramer-von Mises estimates performed better than others. Finally, we observed that precision measures decrease for all estimation techniques when the sample size increases, indicating that all estimation approaches are consistent. Through two real data analyses, the suggested model's validity and adaptability are contrasted with those of other models, including the power inverted Topp–Leone, log-normal, Weibull, generalized exponential, generalized inverse exponential, inverse Weibull, inverse gamma, and extended inverse exponential distributions.

We introduce a new two-parameter model related to the inverted Topp–Leone distribution called the power inverted Topp–Leone (PITL) distribution. Major properties of the PITL distribution are stated; including; quantile measures, moments, moment generating function, probability weighted moments, Bonferroni and Lorenz curve, stochastic ordering, incomplete moments, residual life function, and entropy measure. Acceptance sampling plans are developed for the PITL distribution, when the life test is truncated at a pre-specified time. The truncation time is assumed to be the median lifetime of the PITL distribution with pre-specified factors. The minimum sample size necessary to ensure the specified life test is obtained under a given consumer’s risk. Numerical results for given consumer’s risk, parameters of the PITL distribution and the truncation time are obtained. The estimation of the model parameters is argued using maximum likelihood, least squares, weighted least squares, maximum product of spacing and Bayesian methods. A simulation study is confirmed to evaluate and compare the behavior of different estimates. Two real data applications are afforded in order to examine the flexibility of the proposed model compared with some others distributions. The results show that the power inverted Topp–Leone distribution is the best according to the model selection criteria than other competitive models.

The current work focuses on ranked set sampling and a simple random sample as sampling approaches for determining stress–strength reliability from the inverted Topp–Leone distribution. Asymptotic confidence intervals are established, along with a maximum likelihood estimator of the parameters and stress–strength reliability. The reliability of such a system is assessed using the Bayesian approach under symmetric and asymmetric loss functions. The highest posterior density credible interval is constructed successively. The results are extracted using Monte Carlo simulation to compare the proposed estimators performance with different sample sizes. Finally, by looking at waiting time data and failure times of insulating fluid, the usefulness of the suggested technique is demonstrated.

This study introduces a flexible model with two parameters by combining the type II half-logistic-G family with the inverted Topp–Leone distribution. The proposed model is referred to as the half logistic inverted Topp–Leone (HLITL) distribution. The associated probability density function can be considered a mixture of the inverted Topp–Leone distributions. The proposed model can be deemed an acceptable model for fitting the right-skewed, reversed J-shaped, and unimodal data. The statistical properties, including the moments, Bonferroni and Lorenz curves, Rényi entropy, and quantile function, are derived. Additionally, the plots of the skewness and kurtosis measures are plotted based on the quantiles. The parameter estimators are implemented using the maximum likelihood method based on two sampling schemes: the simple random sample method and the ranked set sampling method. The proposed method is evaluated by using simulations. The results show that the maximum likelihood estimates of the parameters under ranked set sampling are more accurate than those under simple random sampling. Generally, there is good agreement between the theoretical and empirical results. Two real datasets are used to compare the HLITL model with the following models: alpha power exponential, alpha power Lindley, odd Fréchet inverse exponential, and odd Fréchet inverse Rayleigh models. The comparison results show that the HLITL model represents a better alternative lifetime distribution than the other competitive distributions.

In lifetime testing, the failure times of highly reliable products under normal usage conditions are often impractically long, making direct reliability assessment impractical. To overcome this, step-stress partially accelerated life testing is employed to reduce testing time while preserving data quality. This paper develops a Bayesian model based on Type II censored data, assuming that item lifetimes follow the Topp–Leone inverted Kumaraswamy distribution, a flexible alternative to classical lifetime models due to its ability to capture various hazard rate shapes and to model bounded and skewed lifetime data more effectively than traditional models observed in real-world reliability data. Bayes estimators of the model parameters and acceleration factor are derived under both symmetric (balanced squared error) and asymmetric (balanced linear exponential) loss functions using informative priors. The novelty of this work lies in the integration of the Topp–Leone inverted Kumaraswamy distribution within the Bayesian step-stress partially accelerated life testing framework, which has not been explored previously, offering improved modeling capability for complex lifetime data. The proposed method is validated through comprehensive simulation studies under various censoring schemes, demonstrating robustness and superior estimation performance compared to traditional models. A real-data application involving COVID-19 mortality data further illustrates the practical relevance and improved fit of the model. Overall, the results highlight the flexibility, efficiency, and applicability of the proposed Bayesian approach in reliability analysis.

In this article, a new two-parameter model called the truncated Cauchy power-inverted Topp–Leone (TCP-ITL) is constructed by merging the truncated Cauchy power -G (TCP-G) family with the inverted Topp–Leone (ITL) distribution. Some structural properties of the newly suggested model are obtained. Different types of entropies are proposed under the TCP-ITL distribution. Under the complete and hybrid censored data, the maximum likelihood (ML), maximum product of spacing (MPSP), and Bayesian estimate approaches are explored. A simulation study is developed to test the proposed distribution’s restricted sample attributes. In the majority of cases, the numerical data revealed that the Bayesian estimates provided more accurate outcomes than the equivalent alternative estimates. The adaptability of the proposed approach is proven using examples from dependability, medicine, and engineering. A real-world data set is utilized to demonstrate the potential of the TCP-ITL distribution in comparison to other well-known distributions. The results of the model selection revealed that the proposed distribution is the best choice for the data sets under consideration.

In this article, a new three parameters lifetime model called the Topp-Leone Generalized Inverted Exponential (TLGIE) Distribution is introduced. Various properties of the model are derived, including moments, quantile function, survival function, hazard rate function, mean deviation and mode. The method of maximum likelihood is used to estimate the unknown parameters. The properties of the maximum likelihood estimators using Fisher information matrix are studied. Three real data sets are applied for illustrative purpose of this study.