Estimation of Some Lifetime Parameters of Flexible Reduced Logarithmic‐Inverse Lomax Distribution under Progressive Type‐II Censored Data

Buzaridah, Mohamed M.; Ramadan, Dina A.; El-Desouky, B. S.

doi:10.1155/2022/1690458

Cited by 9 publications

(5 citation statements)

References 32 publications

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“…Balakrishnan [10] investigated the characteristics under progressively censored samples and reported that a collection of several advances in the inferential procedures depend on types-I and -II censored samples, Almetwally et al [11] studied the MLE and BE method to determine the parameters of the EGE distribution under progressive censoring. Buzaridah et al [12] and Khalifa et al [13] studied estimations of the distribution parameters under Prog-II censored data and Chen and Gui [14] presented statistical inference of the joint Prog-II censored generalized inverted exponential distribution.…”

Section: Literature Reviewmentioning

confidence: 99%

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Bayesian Inference for Inverse Power Exponentiated Pareto Distribution Using Progressive Type-II Censoring with Application to Flood-Level Data Analysis

Khalifa,

Ramadan,

Alqifari

et al. 2024

Symmetry

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Progressive type-II (Prog-II) censoring schemes are gaining traction in estimating the parameters, and reliability characteristics of lifetime distributions. The focus of this paper is to enhance the accuracy and reliability of such estimations for the inverse power exponentiated Pareto (IPEP) distribution, a flexible extension of the exponentiated Pareto distribution suitable for modeling engineering and medical data. We aim to develop novel statistical inference methods applicable under Prog-II censoring, leading to a deeper understanding of failure time behavior, improved decision-making, and enhanced overall model reliability. Our investigation employs both classical and Bayesian approaches. The classical technique involves constructing maximum likelihood estimators of the model parameters and their bootstrap covariance intervals. Using the Gibbs process constructed by the Metropolis–Hasting sampler technique, the Markov chain Monte Carlo method provides Bayesian estimates of the unknown parameters. In addition, an actual data analysis is carried out to examine the estimation process’s performance under this ideal scheme.

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Section: Literature Reviewmentioning

confidence: 99%

“…Using real datasets provided by Dumonceaux and Antle [12], the 20 flood levels represent a real dataset of Susquehanna River's maximum flood levels at Harrisburg, Pennsylvania, between 1890 and 1969. The data are as follows:…”

Section: Flood-level Datamentioning

confidence: 99%

Bayesian Inference for Inverse Power Exponentiated Pareto Distribution Using Progressive Type-II Censoring with Application to Flood-Level Data Analysis

Khalifa,

Ramadan,

Alqifari

et al. 2024

Symmetry

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“…However, there are difficulties in recognizing the distribution. So far, the well-known methods for estimating the parameters of distribution data are the Method of Moments, the Method of Maximum Likelihood Estimation, the Method of Probability Weighted Moment, and the Richardson Method [9][10][11]. Those methods have some weaknesses [12], including: (1) an iterative procedure for maximum likelihood estimation is based only on a complete sample of various population parameters; (2) the solution is only based on a linear system; (3) the method cannot find the precise parameter if the system has more than one peak (4), the method cannot find the parameter if the distribution members are infinite, (5) the solution requires complex mathematical solving skills, such as integral approach [13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

The Modification of Chi-Square Tests for the Identification of Rainfall and River Flow Data Distribution

Sulistiyono¹,

Yasa²,

Setiawan³

et al. 2023

cea

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The growing population in the community has led to an increase in the need for community infrastructure. Civil engineers have to maintain the safety of the community in the design of urban areas' service infrastructure. The infrastructure must resist the load caused by extreme events, such as rainstorms and floods. Therefore, civil engineers must design the infrastructure based on the precise data parameters. Engineers obtain the precise parameters of a return period through frequency analysis. The precise parameters will produce an acceptable data distribution. Civil engineers can use the Chi-Square method to test the fitness of the data distribution type. However, the original way to get the Expected Frequency is complicated because it uses the integral solving method. This weakness causes the engineers to linger to test the distribution suitability. This article proposes a modification to ease obtaining the expected frequency in the Chi-Square test. This article demonstrates the proposal using rainfall and river flow data around the globe. The demonstration results show that the proposal is easy to implement. The method accurately identifies the type of rainfall and river flow data distribution. Among the seven stations, five groups of data follow a lognormal distribution; one group of data follows a normal distribution. One other group of data follows an exponential distribution.

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“…, S r ) are predetermined and fixed. A useful description and good summary of progressive censoring (PC) can be found in [23][24][25][26][27][28][29][30][31][32][33][34]. It should be noted that, when S 1 = S 2 = .…”

Section: Introductionmentioning

confidence: 99%

A New Asymmetric Modified Topp–Leone Distribution: Classical and Bayesian Estimations under Progressive Type-II Censored Data with Applications

et al. 2023

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In this article, a new modified asymmetric Topp–Leone distribution is created and developed from a theoretical and inferential point of view. It has the feature of extending the remarkable flexibility of a special one-shape-parameter lifetime distribution, known as the inverse Topp–Leone distribution, to the bounded interval [0, 1]. The probability density function of the proposed truncated distribution has the potential to be unimodal and right-skewed, with different levels of asymmetry. On the other hand, its hazard rate function can be increasingly shaped. Some important statistical properties are examined, including several different measures. In practice, the estimation of the model parameters under progressive type-II censoring is considered. To achieve this aim, the maximum likelihood, maximum product of spacings, and Bayesian approaches are used. The Markov chain Monte Carlo approach is employed to produce the Bayesian estimates under the squared error and linear exponential loss functions. Some simulation studies to evaluate these approaches are discussed. Two applications based on real-world datasets—one on the times of infection, and the second dataset is on trading economics credit rating—are considered. Thanks to its flexible asymmetric features, the new model is preferable to some known comparable models.

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Estimation of Some Lifetime Parameters of Flexible Reduced Logarithmic‐Inverse Lomax Distribution under Progressive Type‐II Censored Data

Cited by 9 publications

References 32 publications

Bayesian Inference for Inverse Power Exponentiated Pareto Distribution Using Progressive Type-II Censoring with Application to Flood-Level Data Analysis

Bayesian Inference for Inverse Power Exponentiated Pareto Distribution Using Progressive Type-II Censoring with Application to Flood-Level Data Analysis

The Modification of Chi-Square Tests for the Identification of Rainfall and River Flow Data Distribution

A New Asymmetric Modified Topp–Leone Distribution: Classical and Bayesian Estimations under Progressive Type-II Censored Data with Applications

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