A better approach to discuss medical science and engineering data with a modified Lehmann Type – II model

Background: Modeling with the complex random phenomena that are frequently observed in reliability engineering, hydrology, ecology, medical science, and agricultural sciences was once thought to be an enigma. Scientists and practitioners agree that an appropriate but simple model is the best choice for this investigation. To address these issues, scientists have previously discussed a variety of bounded and unbounded, simple to complex lifetime models. Methods: We discussed a modified Lehmann type II (ML-II) model as a better approach to modeling bathtub-shaped and asymmetric random phenomena. A number of complementary mathematical and reliability measures were developed and discussed. Furthermore, explicit expressions for the moments, quantile function, and order statistics were developed. Then, we discussed the various shapes of the density and reliability functions over various model parameter choices. The maximum likelihood estimation (MLE) method was used to estimate the unknown model parameters, and a simulation study was carried out to evaluate the MLEs' asymptotic behavior. Results: We demonstrated ML- II's dominance over well-known competitors by modeling anxiety in women and electronic data.

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A new modified Lehmann type – II G class of distributions: exponential distribution with theory, simulation, and applications to engineering sector

F1000Research ◽

10.12688/f1000research.52494.1 ◽

2021 ◽

Vol 10 ◽

pp. 483

Author(s):

Oluwafemi Samson Balogun ◽

Muhammad Zeshan Arshad ◽

Muhammad Zafar Iqbal ◽

Madiha Ghamkhar

Keyword(s):

Exponential Distribution ◽

Goodness Of Fit ◽

Likelihood Estimation ◽

Quantile Function ◽

Model Parameters ◽

Type Ii ◽

Reliability Engineering ◽

New Members ◽

Anderson Darling ◽

Von Mises

Background: Modeling against non-normal data a challenge for theoretical and applied scientists to choose a lifetime model and expect to perform optimally against experimental, reliability engineering, hydrology, ecology, and agriculture sciences, phenomena. Method: We have introduced a new G class that generates relatively more flexible models to its baseline and we refer to it as the new modified Lehmann Type – II (ML–II) G class of distributions. A list of new members of ML–II-G class is developed and as a sub-model the exponential distribution, known as the ML-II-Exp distribution is considered for further discussion. Several mathematical and reliability characters along with explicit expressions for moments, quantile function, and order statistics are derived and discussed in detail. Furthermore, plots of density and hazard rate functions are sketched out over the certain choices of the parametric values. For the estimation of the model parameters, we utilized the method of maximum likelihood estimation. Results: The applicability of the ML–II–G class is evaluated via ML–II–Exp distribution. ML–II–Exp distribution is modeled to four suitable lifetime datasets and the results are compared with the well-known competing models. Some well recognized goodness–of–fit including -Log-likelihood (-LL), Anderson-Darling (A*), Cramer-Von Mises (W*), and Kolmogorov-Smirnov (K-S) test statistics are considered for the selection of a better fit model. Conclusion: The minimum value of the goodness–of–fit is the criteria of a better fit model that the ML–II–Exp distribution perfectly satisfies. Hence, we affirm that the ML–II–Exp distribution is a better fit model than its competitors.

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A New Gamma Generalized Lindley-Log- logistic Distribution with Applications

Afrika Statistika ◽

10.16929/as/2020.2451.168 ◽

2020 ◽

Vol 15 (4) ◽

pp. 2451-2479

Author(s):

Broderick Olusegun Oluyede ◽

Thatayaone Moakofi ◽

Boikanyo Makubate

Keyword(s):

Maximum Likelihood ◽

Hazard Function ◽

Maximum Likelihood Estimators ◽

Likelihood Estimation ◽

Quantile Function ◽

Logistic Distribution ◽

Model Parameters ◽

Lorenz Curves ◽

Conditional Moments ◽

New Distribution

A new distribution called the gamma exponentiated Lindley Log-logistic (GELLLoG) distribution is developed. Some properties of the new distribution including hazard function, quantile function, moments, conditional moments, mean and median deviations, Bonferroni and Lorenz curves, distribution of the order statistics and Réenyi entropy are derived. Maximum likelihood estimation technique is used to estimate the model parameters. We conduct a simulation study to examine the bias and mean square error of the maximum likelihood estimators. Finally, applications to real datasets to illustrate the usefulness of the proposed distribution are presented.

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Type II Power Topp-Leone Generated Family of Distributions with Statistical Inference and Applications

Symmetry ◽

10.3390/sym12010075 ◽

2020 ◽

Vol 12 (1) ◽

pp. 75 ◽

Cited By ~ 3

Author(s):

Rashad A. R. Bantan ◽

Farrukh Jamal ◽

Christophe Chesneau ◽

Mohammed Elgarhy

Keyword(s):

Natural Extension ◽

Stochastic Ordering ◽

Quantile Function ◽

Model Parameters ◽

Data Sets ◽

Type Ii ◽

New Family ◽

The Family ◽

Family Based ◽

High Level

In this paper, we present and study a new family of continuous distributions, called the type II power Topp-Leone-G family. It provides a natural extension of the so-called type II Topp-Leone-G family, thanks to the use of an additional shape parameter. We determine the main properties of the new family, showing how they depend on the involving parameters. The following points are investigated: shapes and asymptotes of some important functions, quantile function, some mixture representations, moments and derivations, stochastic ordering, reliability and order statistics. Then, a special model of the family based on the inverse exponential distribution is introduced. It is of particular interest because the related probability functions are tractable and possess various kinds of asymmetric shapes. Specially, reverse J, left skewed, near symmetrical and right skewed shapes are observed for the corresponding probability density function. The estimation of the model parameters is performed by the use of three different methods. A complete simulation study is proposed to illustrate their numerical efficiency. The considered model is also applied to analyze two different kinds of data sets. We show that it outperforms other well-known models defined with the same baseline distribution, proving its high level of adaptability in the context of data analysis.

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Type II Half Logistic Linear Failure Rate Distribution with Application

Journal of Computational and Theoretical Nanoscience ◽

10.1166/jctn.2020.9178 ◽

2020 ◽

Vol 17 (7) ◽

pp. 2912-2917

Author(s):

Maha A. Aldahlan

Keyword(s):

Failure Rate ◽

Probability Distributions ◽

Estimation Method ◽

Likelihood Estimation ◽

Real Data ◽

Model Parameters ◽

Type Ii ◽

Data Set ◽

Rate Distribution ◽

New Distribution

In recent years, several of new improved probability distributions have been discovered from the current distributions to facilitate their applications in various areas. A new three-parameter model extended from the linear failure rate model, the so called the type II half logistic linear failure rate distribution. Some mathematical properties of the new distribution are proposed. Explicit expressions for the moments, probability weighted moments and order statistics are calculated. Maximum likelihood estimation method is assessed to estimate the model parameters are presented. The superiority of the new distribution is illustrated with an application to one real data set.

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Sine Inverse Lomax Generated Family of Distributions with Applications

Mathematical Problems in Engineering ◽

10.1155/2021/1267420 ◽

2021 ◽

Vol 2021 ◽

pp. 1-11

Author(s):

Aisha Fayomi ◽

Ali Algarni ◽

Abdullah M. Almarashi

Keyword(s):

Maximum Likelihood ◽

Real Life ◽

Likelihood Estimation ◽

Quantile Function ◽

Maximum Likelihood Estimates ◽

Model Parameters ◽

New Family ◽

Estimation Of Model Parameters ◽

Generated Family ◽

Family Of Distributions

This paper introduces a new family of distributions by combining the sine produced family and the inverse Lomax generated family. The new proposed family is very interested and flexible more than some old and current families. It has many new models which have many applications in physics, engineering, and medicine. Some fundamental statistical properties of the sine inverse Lomax generated family of distributions as moments, generating function, and quantile function are calculated. Four special models as sine inverse Lomax-exponential, sine inverse Lomax-Rayleigh, sine inverse Lomax-Frèchet and sine inverse Lomax-Lomax models are proposed. Maximum likelihood estimation of model parameters is proposed in this paper. For the purpose of evaluating the performance of maximum likelihood estimates, a simulation study is conducted. Two real life datasets are analyzed by the sine inverse Lomax-Lomax model, and we show that providing flexibility and more fitting than known nine models derived from other generated families.

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Generalized Beta-Exponential Weibull Distribution and its Applications

Journal of Statistics Advances in Theory and Applications ◽

10.18642/jsata_7100122158 ◽

2020 ◽

Vol 24 (1) ◽

pp. 1-33

Author(s):

N. I. Badmus ◽

◽

Olanrewaju Faweya ◽

K. A. Adeleke ◽

◽

...

Keyword(s):

Weibull Distribution ◽

Information Matrix ◽

Estimation Method ◽

Likelihood Estimation ◽

Real Data ◽

Quantile Function ◽

Model Parameters ◽

Data Sets ◽

Hazard Functions ◽

Generalized Distributions

In this article, we investigate a distribution called the generalized beta-exponential Weibull distribution. Beta exponential x family of link function which is generated from family of generalized distributions is used in generating the new distribution. Its density and hazard functions have different shapes and contains special case of distributions that have been proposed in literature such as beta-Weibull, beta exponential, exponentiated-Weibull and exponentiated-exponential distribution. Various properties of the distribution were obtained namely; moments, generating function, Renyi entropy and quantile function. Estimation of model parameters through maximum likelihood estimation method and observed information matrix are derived. Thereafter, the proposed distribution is illustrated with applications to two different real data sets. Lastly, the distribution clearly shown that is better fitted to the two data sets than other distributions.

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Maximum Likelihood Estimation of the VAR(1) Model Parameters with Missing Observations

Mathematical Problems in Engineering ◽

10.1155/2013/848120 ◽

2013 ◽

Vol 2013 ◽

pp. 1-13 ◽

Cited By ~ 2

Author(s):

Helena Mouriño ◽

Maria Isabel Barão

Keyword(s):

Stochastic Process ◽

Missing Data ◽

Maximum Likelihood ◽

Moving Average ◽

Practical Importance ◽

Likelihood Estimation ◽

Model Parameters ◽

Missing Observations ◽

Data Set ◽

The Impact

Missing-data problems are extremely common in practice. To achieve reliable inferential results, we need to take into account this feature of the data. Suppose that the univariate data set under analysis has missing observations. This paper examines the impact of selecting an auxiliary complete data set—whose underlying stochastic process is to some extent interdependent with the former—to improve the efficiency of the estimators for the relevant parameters of the model. The Vector AutoRegressive (VAR) Model has revealed to be an extremely useful tool in capturing the dynamics of bivariate time series. We propose maximum likelihood estimators for the parameters of the VAR(1) Model based on monotone missing data pattern. Estimators’ precision is also derived. Afterwards, we compare the bivariate modelling scheme with its univariate counterpart. More precisely, the univariate data set with missing observations will be modelled by an AutoRegressive Moving Average (ARMA(2,1)) Model. We will also analyse the behaviour of the AutoRegressive Model of order one, AR(1), due to its practical importance. We focus on the mean value of the main stochastic process. By simulation studies, we conclude that the estimator based on the VAR(1) Model is preferable to those derived from the univariate context.

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