Generalized Mixtures of Exponential Distribution and Associated Inference

Yang, Yaoting; Tian, Weizhong; Tong, Tingting

doi:10.3390/math9121371

Cited by 8 publications

(7 citation statements)

References 18 publications

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“…In this example we have applied our proposed control chart to data set represents the survival times of 121 patients with breast cancer obtained from a large hospital during the time of 1929 to 1938. This data set has recently been used by [17].…”

Section: Application To Survival Time Of Breast Cancer Patientsmentioning

confidence: 99%

Advancing Quality Assurance In Manufacturing: A Weighted Exponential Distribution Control Chart For Enhanced Production Monitoring

Iqbal,

Kashif

et al. 2024

Migrat. Lett.

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Over the last few decades, weighted distributions have received substantial attention from researchers due to their utility across a range of research fields. With an emphasis on the relevance of weighted distributions, a new control chart for a weighted exponentially distributed characteristic using an exponentially weighted moving average (EWMA) has been proposed in this manuscript. The average run length of both in-control and out-of-control processes has been derived. The efficiency of the proposed control chart has been compared with existing chart based on the unweighted exponential distribution in terms of Average Run Length (ARL) and the percentage decrease in ARL (ΔARL) using Monte Carlo Simulations. Furthermore, the proposed control chart has been applied to various real-life applications to highlight its applicability in industrial and manufacturing processes.

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Section: Application To Survival Time Of Breast Cancer Patientsmentioning

confidence: 99%

Advancing Quality Assurance In Manufacturing: A Weighted Exponential Distribution Control Chart For Enhanced Production Monitoring

Iqbal,

Kashif

et al. 2024

Migrat. Lett.

View full text Add to dashboard Cite

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“…(i) The cdf can be written as F o (x; α, λ) = aF(x; λ) + bF(x; λ(α + 1)), where a = (α + 2)/(α + 1) > 0 and b = −1/(α + 1) < 0, meaning that the MWE distribution also belongs to the family of generalized mixture of two exponential distributions, following the spirit of the distribution proposed by [16], (ii) The cdf is quite simple to manage and consequently, the MWE distribution can be studied in an-depth manner on all the theoretical and practical aspects, (iii) Thanks to the parameter α, the related pdf can be decreasing or unimodal, and the related hrf can be constant or increasing as proven later, (iv) In some concrete scenarios, the MWE model can be more efficient in data fitting than the exponential or WE models, among other lifetime models.…”

Section: Contributionsmentioning

confidence: 99%

“…Recently, Oguntunde et al [12] proposed a two-parameter inverted WE distribution, Mallick et al [13] supplemented a new bounded distribution using the structure of the WE distribution and Bakouch et al [14] proposed a new kind of weighted exponential distribution with the feature of logarithmic weight function. Further discussions on the WE distribution can be found in [15,16], and the references therein.…”

Section: Introduction 1state Of Artmentioning

confidence: 99%

On a Modified Weighted Exponential Distribution with Applications

Chesneau

Kumar

Khetan

et al. 2022

MCA

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Practitioners in all applied domains value simple and adaptable lifetime distributions. They make it possible to create statistical models that are relatively easy to manage. A novel simple lifetime distribution with two parameters is proposed in this article. It is based on a parametric mixture of the exponential and weighted exponential distributions, with a mixture weight depending on a parameter of the involved distribution; no extra parameter is added in this mixture operation. It can also be viewed as a special generalized mixture of two exponential distributions. This decision is based on sound mathematical and physical reasoning; the weight modification allows us to combine some joint properties of the exponential and weighted exponential distribution, which are known as complementary in several modeling aspects. As a result, the proposed distribution may have a decreasing or unimodal probability density function and possess the demanded increasing hazard rate property. Other properties are studied, such as the moments, Bonferroni and Lorenz curves, Rényi entropy, stress-strength reliability, and mean residual life function. Subsequently, a part is devoted to the associated model, which demonstrates how it can be used in a real-world statistical scenario involving data. In this regard, we demonstrate how the estimated model performs well using five different estimation methods and simulated data. The analysis of two data sets demonstrates these excellent results. The new model is compared to the weighted exponential, Weibull, gamma, and generalized exponential models for performance. The obtained comparison results are overwhelmingly in favor of the proposed model according to some standard criteria.

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“…Fifth data set: This data obtained from [41] which report the survival times of 121 breast cancer patients in the period between 1929 to 1938, see Table 12 in the Appendix.…”

Section: Applicationsmentioning

confidence: 99%

A New Generalization of the Exponentiated Fréchet Distribution with Applications

Baharith

2022

JRSS

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The addition of an extra parameter to standard distributions is a common technique in statistical theory. This study introduces a new generalization of the Exponentiated Fréchet distribution named alpha power exponentiated Fréchet distribution (APEF). The APEF allows for a significant amount of versatility in modeling various data forms as it accommodates upside-down bathtubs, decreasing, and reversed-J shapes for hazard rate function. Some of the APEF’s mathematical properties are derived in close forms. The maximum likelihood technique is used to estimate the new distribution parameters. Numerical results are calculated to demonstrate the estimators’ performance. Five well-known real-life applications show the flexibility and potentiality of the APEF empirically. The APEF outperforms other competing distributions based on model selection criteria.

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Generalized Mixtures of Exponential Distribution and Associated Inference

Cited by 8 publications

References 18 publications

Advancing Quality Assurance In Manufacturing: A Weighted Exponential Distribution Control Chart For Enhanced Production Monitoring

Advancing Quality Assurance In Manufacturing: A Weighted Exponential Distribution Control Chart For Enhanced Production Monitoring

On a Modified Weighted Exponential Distribution with Applications

A New Generalization of the Exponentiated Fréchet Distribution with Applications

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