A Non-Mixture Cure Model for Right-Censored Data with Fréchet Distribution

This paper considers a non-mixture cure model for right-censored data. It utilizes the maximum likelihood method to estimate model parameters in the non-mixture cure model. The simulation study is based on Fréchet susceptible distribution to evaluate the performance of the method. Compared with Weibull and exponentiated exponential distributions, the non-mixture Fréchet distribution is shown to be the best in modeling a real data on allogeneic marrow HLA-matched donors and ECOG phase III clinical trial e1684 data.

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A Non-Mixture Cure Model for Right Censored Data with Fréchet Distribution

10.20944/preprints201809.0588.v1 ◽

2018 ◽

Author(s):

Durga Kutal ◽

Lianfen Qian

Keyword(s):

Censored Data ◽

Real Data ◽

Phase Iii ◽

Likelihood Method ◽

Model Parameters ◽

Exponential Distributions ◽

Right Censored Data ◽

Cure Model ◽

Mixture Cure Model ◽

Allogeneic Marrow

This paper considers a non-mixture cure model for right censored data. It utilizes the maximum likelihood method to estimate model parameters in the non-mixture cure model. The simulation study is based on Fréchet susceptible distribution to evaluate the performance of the method. Comparing with Weibull and exponentiated exponential distributions, the non-mixture Fréchet distribution is shown to be the best in modeling a real data on allogeneic marrow HLA-matched donors and ECOG phase III clinical trial e1684 data.

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The four-parameter Fréchet distribution: Properties and applications

Pakistan Journal of Statistics and Operation Research ◽

10.18187/pjsor.v16i2.3097 ◽

2020 ◽

pp. 249-264

Author(s):

Mohamed Hamed ◽

Fahad Aldossary ◽

Ahmed Z. Afify

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Method ◽

Real Data ◽

Maximum Likelihood Estimates ◽

Likelihood Method ◽

Model Parameters ◽

Fréchet Distribution ◽

Mathematical Properties ◽

Modeling Data ◽

Frechet Distribution

In this article, we propose a new four-parameter Fréchet distribution called the odd Lomax Fréchet distribution. The new model can be expressed as a linear mixture of Fréchet densities. We provide some of its mathematical properties. The estimation of the model parameters is performed by the maximum likelihood method. We illustrate the good performance of the maximum likelihood estimates via a detailed numerical simulation study. The importance and usefulness of the proposed distribution for modeling data are illustrated using two real data applications.

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The Beta Exponential Fréchet Distribution with Applications

Austrian Journal of Statistics ◽

10.17713/ajs.v46i1.144 ◽

2017 ◽

Vol 46 (1) ◽

pp. 41-63 ◽

Cited By ~ 6

Author(s):

M.E. Mead ◽

Ahmed Z. Afify ◽

G.G. Hamedani ◽

Indranil Ghosh

Keyword(s):

Residual Life ◽

Real Data ◽

Mean Residual Life ◽

Model Parameters ◽

Data Sets ◽

Nested Models ◽

Fréchet Distribution ◽

Proposed Model ◽

Mean Inactivity Time ◽

Frechet Distribution

We define and study a new generalization of the Fréchet distribution called the beta exponential Fréchet distribution. The new model includes thirty two special models. Some of its mathematical properties, including explicit expressions for the ordinary and incomplete moments, quantile and generating functions, mean residual life, mean inactivity time, order statistics and entropies are derived. The method of maximum likelihood is proposed to estimate the model parameters. A small simulation study is alsoreported. Two real data sets are applied to illustrate the flexibility of the proposed model compared with some nested and non-nested models.

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The Reflected-Shifted-Truncated Lindley Distribution with Applications

Stochastics and Quality Control ◽

10.1515/eqc-2020-0008 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Sanku Dey ◽

Sophia Waymyers ◽

Devendra Kumar

Keyword(s):

Maximum Likelihood ◽

Censored Data ◽

Real Data ◽

Comprehensive Treatment ◽

Model Parameters ◽

Data Sets ◽

Right Censored Data ◽

Lindley Distribution ◽

Failure Data ◽

Maximum Likelihood Methods

AbstractIn this paper, a new probability density function with bounded domain is presented. The new distribution arises from the Lindley distribution proposed in 1958. It presents the advantage of not including any special function in its formulation. The new transformed model, called the reflected-shifted-truncated Lindley distribution can be used to model left-skewed data. We provide a comprehensive treatment of general mathematical and statistical properties of this distribution. We estimate the model parameters by maximum likelihood methods based on complete and right-censored data. To assess the performance and consistency of the maximum likelihood estimators, we conduct a simulation study with varying sample sizes. Finally, we use the distribution to model left-skewed survival and failure data from two real data sets. For the real data sets containing complete data and right-censored data, this distribution is superior in its ability to sufficiently model the data as compared to the power Lindley, exponentiated power Lindley, generalized inverse Lindley, generalized weighted Lindley and the well-known Gompertz distributions.

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Generalized Exponential Power Distribution with Application to Complete and Censored Data

Asian Journal of Probability and Statistics ◽

10.9734/ajpas/2021/v12i130278 ◽

2021 ◽

pp. 34-55

Author(s):

M. M. E. Abd El-Monsef ◽

M. M. El-Awady

Keyword(s):

Maximum Likelihood ◽

Censored Data ◽

Power Distribution ◽

Real Data ◽

Likelihood Method ◽

Model Parameters ◽

Type I ◽

Sample Type ◽

Exponential Power Distribution ◽

Exponential Power

The exponential power distribution (EP) is a lifetime model that can exhibit increasing and bathtub hazard rate function. This paper proposed a generalization of EP distribution, named generalized exponential power (GEP) distribution. Some properties of GEP distribution will be investigated. Recurrence relations for single moments of generalized ordered statistics from GEP distribution are established and used for characterizing the GEP distribution. Estimation of the model parameters are derived using maximum likelihood method based on complete sample, type I, type II and random censored samples. A simulation study is performed in order to examine the accuracy of the maximum likelihood estimators of the model parameters. Three applications to real data, two with censored data, are provided in order to show the superiority of the proposed model to other models.

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Theory and Applications of the Unit Gamma/Gompertz Distribution

Mathematics ◽

10.3390/math9161850 ◽

2021 ◽

Vol 9 (16) ◽

pp. 1850

Author(s):

Rashad A. R. Bantan ◽

Farrukh Jamal ◽

Christophe Chesneau ◽

Mohammed Elgarhy

Keyword(s):

Stochastic Ordering ◽

Real Data ◽

Rate Function ◽

The Other ◽

Likelihood Method ◽

Model Parameters ◽

Data Sets ◽

Gompertz Distribution ◽

Probability And Statistics ◽

Analytical Behavior

Unit distributions are commonly used in probability and statistics to describe useful quantities with values between 0 and 1, such as proportions, probabilities, and percentages. Some unit distributions are defined in a natural analytical manner, and the others are derived through the transformation of an existing distribution defined in a greater domain. In this article, we introduce the unit gamma/Gompertz distribution, founded on the inverse-exponential scheme and the gamma/Gompertz distribution. The gamma/Gompertz distribution is known to be a very flexible three-parameter lifetime distribution, and we aim to transpose this flexibility to the unit interval. First, we check this aspect with the analytical behavior of the primary functions. It is shown that the probability density function can be increasing, decreasing, “increasing-decreasing” and “decreasing-increasing”, with pliant asymmetric properties. On the other hand, the hazard rate function has monotonically increasing, decreasing, or constant shapes. We complete the theoretical part with some propositions on stochastic ordering, moments, quantiles, and the reliability coefficient. Practically, to estimate the model parameters from unit data, the maximum likelihood method is used. We present some simulation results to evaluate this method. Two applications using real data sets, one on trade shares and the other on flood levels, demonstrate the importance of the new model when compared to other unit models.

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New Acceptance Sampling Plans Based on Percentiles for Exponentiated Fréchet Distribution

Economic Quality Control ◽

10.1515/eqc-2015-0011 ◽

2016 ◽

Vol 31 (1) ◽

Cited By ~ 1

Author(s):

Gadde Srinivasa Rao ◽

Kanaparthi Rosaiah ◽

Mothukuri Sridhar Babu ◽

Devireddy Charanaudaya Sivakumar

Keyword(s):

Operating Characteristic ◽

Real Data ◽

Acceptance Sampling ◽

Producer’S Risk ◽

Data Set ◽

Sampling Plans ◽

Fréchet Distribution ◽

Acceptance Sampling Plans ◽

Characteristic Values ◽

Frechet Distribution

AbstractIn this article, acceptance sampling plans are developed for the exponentiated Fréchet distribution based on percentiles when the life test is truncated at a pre-specified time. The minimum sample size necessary to ensure the specified life percentile is obtained under a given customer's risk and producer's risk simultaneously. The operating characteristic values of the sampling plans are presented. One example with real data set is also given as an illustration.

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Mixture of Inverse Weibull and Lognormal Distributions: Properties, Estimation, and Illustration

Mathematical Problems in Engineering ◽

10.1155/2015/526786 ◽

2015 ◽

Vol 2015 ◽

pp. 1-8 ◽

Cited By ~ 2

Author(s):

K. S. Sultan ◽

A. S. Al-Moisheer

Keyword(s):

Information Matrix ◽

Real Data ◽

Likelihood Method ◽

Model Parameters ◽

Component Mixture ◽

Data Set ◽

Hazard Functions ◽

Lognormal Distributions ◽

Proposed Model ◽

Estimation Of Model Parameters

We discuss the two-component mixture of the inverse Weibull and lognormal distributions (MIWLND) as a lifetime model. First, we discuss the properties of the proposed model including the reliability and hazard functions. Next, we discuss the estimation of model parameters by using the maximum likelihood method (MLEs). We also derive expressions for the elements of the Fisher information matrix. Next, we demonstrate the usefulness of the proposed model by fitting it to a real data set. Finally, we draw some concluding remarks.

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