scholarly journals Study of a unit power-logarithmic distribution

2021 ◽  
Vol 5 (1) ◽  
pp. 218-235
Author(s):  
Christophe Chesneau ◽  
Keyword(s):  
Stochastic Order ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Rate Function ◽  
Cumulative Distribution ◽  
Functional Capabilities ◽  
Logarithmic Distribution ◽  
Logarithmic Functions ◽  
Mean Variance ◽  
Selection Of

This article proposes a new unit distribution based on the power-logarithmic scheme. The corresponding cumulative distribution function is defined by a special ratio of power and logarithmic functions that is dependent on one parameter. We show that this function benefits from great flexibility characterized by a large selection of convex and concave shapes. The other key functions are determined and studied. In particular, we show that the probability density function may take on different decreasing or U shapes, and the hazard rate function has a wide panel of U shapes. These functional capabilities are rare for a one-parameter unit distribution. In addition, we prove certain stochastic order results, provide the expression of the quantile function via the Lambert function, some interesting distributional results, and give simple expressions for the ordinary moments, mean, variance, skewness, kurtosis, moment generating function and incomplete moments. Subsequently, a basic statistical approach is described, to show how the new distribution can be applied in a data analysis scenario. Finally, complementary mathematical findings are presented, yielding new integrals linked to the Euler constant via some well-known moments properties.

scholarly journals Transmutation of the two parameters Rayleigh distribution

2016 ◽  
Vol 4 (2) ◽  
pp. 95
Author(s):  
Ehsan Ullah ◽  
Mirza Shahzad
Keyword(s):  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Rayleigh Distribution ◽  
Least Square ◽  
Least Square Estimation ◽  
Proposed Model ◽  
Method Of Least Square ◽  
Two Parameters ◽  
Mean Variance

In this study, transmuted two parameters Rayleigh distribution is proposed using quadratic rank transmutation map. This proposed distribution is more flexible and versatile than two parameters Rayleigh distribution. Some properties of the proposed distribution are derived such as moments, moment generating function, mean, variance, median, quantile function, reliability, and hazard function. The parameter estimation is approached through the method of least square estimation. The th and joint order statistics are also derived for the proposed distribution. The application of proposed model illustrated and compared using real data.

THE MAXIMUM FAILURE TIME DISTRIBUTION

2009 ◽  
Vol 09 (02) ◽  
pp. 369-381
Author(s):  
SARALEES NADARAJAH ◽  
SAMUEL KOTZ
Keyword(s):  
Failure Time ◽  
Moment Generating Function ◽  
Rate Function ◽  
Cumulative Distribution ◽  
Mean Deviation ◽  
Exact Probability ◽  
Failure Time Distribution ◽  
Failure Times ◽  
Exact Probability Distribution ◽  
Methods Of Moments

For systems with parallel components, the variable of primary importance is the maximum of the failure times of the different components. In this paper, we study the exact probability distribution of the maximum failure time. Explicit expressions are derived for the cumulative distribution function, probability density function, hazard rate function, moment-generating function, nth moment, variance, skewness, kurtosis, mean deviation, Shannon entropy, and the order statistics. Estimation procedures are derived by the methods of moments and maximum likelihood. We expect that these results could be useful for performance assessment of parallel systems.

scholarly journals A Four-Parameter Extension of Burr III Distribution with Applications

2021 ◽  
Vol 3 (1) ◽  
pp. 7-19
Author(s):  
Emmanuel W. Okereke ◽  
Johnson Ohakwe
Keyword(s):  
Maximum Likelihood ◽  
Hazard Rate ◽  
Linear Representation ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Rate Function ◽  
Hazard Rate Function ◽  
Maximum Likelihood Procedure ◽  
Burr Iii Distribution ◽  
New Distribution

AbstractIn this paper, we defined and studied a new distribution called the odd exponentiated half-logistic Burr III distribution. Properties such as the linear representation of the probability density function (PDF) of the distribution, quantile function, ordinary and incomplete moments, moment generating function and distribution of the order statistic were derived. The PDF and hazard rate function were found to be capable of having various shapes, making the new distribution highly flexible. In particular, the hazard rate function can be nonincreasing, unimodal and nondecreasing. It can also have the bathtub shape among other non- monotone shapes. The maximum likelihood procedure was used to estimate the parameters of the new model. We gave two numerical examples to illustrate the usefulness and the ability of the distribution to provide better fits to a number of data sets than several distributions in existence.Keywords: Burr III distribution; maximum likelihood procedure; moments; odd exponentiated half-logistic-G family; order statistics. AbstrakPada artikel ini akan didefinisikan dan dipelajari mengenai distribusi baru yang disebut distribusi Burr III setengah logistik tereksponen ganjil. Kami menurunkan beberapa sifat dari distribusi tersebut yaitu representasi linier dari fungsi kepadatan peluang (FKP), fungsi kuantil, momen biasa dan momen tidak lengkap, fungsi pembangkit momen dan distribusi statistik terurut. Fungsi FKP dan fungsi tingkat hazard diperoleh memiliki bermacam-macam bentuk, membuat distribusi baru ini sangat fleksibel. Secara khusus, fungsi tingkat hazard dapat berupa fungsi taknaik, bermodus tunggal, bisa juga tidak turun. Selain itu, fungsi ini juga dapat berbentuk seperti bak mandi di antara bentuk-bentuk tak monoton lainnya. Prosedur kemungkinan maksimum digunakan untuk mengestimasi parameter model yang baru. Kami memberikan dua contoh numerik untuk mengilustrasikan kegunaan dan kemampuan distribusi untuk menghasilkan kesesuaian yang lebih baik pada sejumlah kumpulan data dibandingkan beberapa distribusi yang ada.Kata kunci: distribusi Burr III; prosedur kemungkinan maksimum; momen; keluarga setengah logistik-G teresponen ganjil; statistic terurut.

scholarly journals Estimation of Sine Inverse Exponential Model under Censored Schemes

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
M. Shrahili ◽  
I. Elbatal ◽  
Waleed Almutiry ◽  
Mohammed Elgarhy
Keyword(s):  
Hazard Rate ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Data Fitting ◽  
Exponential Model ◽  
Rate Function ◽  
Numerical Results ◽  
Conditional Moments ◽  
Censored Samples ◽  
Distribution Parameters

In this article, we introduce a new one-parameter model, which is named sine inverted exponential (SIE) distribution. The SIE distribution is a new extension of the inverse exponential (IE) distribution. The SIE distribution aims to provide the SIE model for data-fitting purposes. The SIE distribution is more flexible than the inverted exponential (IE) model, and it has many applications in physics, medicine, engineering, nanophysics, and nanoscience. The density function (PDFu) of SIE distribution can be unimodel shape and right skewed shape. The hazard rate function (HRFu) of SIE distribution can be J-shaped and increasing shaped. We investigated some fundamental statistical properties such as quantile function (QFu), moments (Mo), moment generating function (MGFu), incomplete moments (ICMo), conditional moments (CMo), and the SIE distribution parameters were estimated using the maximum likelihood (ML) method for estimation under censored samples (CS). Finally, the numerical results were investigated to evaluate the flexibility of the new model. The SIE distribution and the IE distribution are compared using two real datasets. The numerical results show the superiority of the SIE distribution.

scholarly journals Exponentiated Generalized Inverted Gompertz Distribution: Properties and Estimation Methods with Applications to Symmetric and Asymmetric Data

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1868
Author(s):  
Mahmoud El-Morshedy ◽  
Adel A. El-Faheem ◽  
Afrah Al-Bossly ◽  
Mohamed El-Dawoody
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Quantile Function ◽  
Reliability Function ◽  
Moment Generating Function ◽  
Rate Function ◽  
Estimation Methods ◽  
Gompertz Distribution ◽  
Asymmetric Data ◽  
Von Mises

In this article, a new four-parameter lifetime model called the exponentiated generalized inverted Gompertz distribution is studied and proposed. The newly proposed distribution is able to model the lifetimes with upside-down bathtub-shaped hazard rates and is suitable for describing the negative and positive skewness. A detailed description of some various properties of this model, including the reliability function, hazard rate function, quantile function, and median, mode, moments, moment generating function, entropies, kurtosis, and skewness, mean waiting lifetime, and others are presented. The parameters of the studied model are appreciated using four various estimation methods, the maximum likelihood, least squares, weighted least squares, and Cramér-von Mises methods. A simulation study is carried out to examine the performance of the new model estimators based on the four estimation methods using the mean squared errors (MSEs) and the bias estimates. The flexibility of the proposed model is clarified by studying four different engineering applications to symmetric and asymmetric data, and it is found that this model is more flexible and works quite well for modeling these data.

scholarly journals The Hamza Distribution with Statistical Properties and Applications

2020 ◽  
pp. 28-42
Author(s):  
Ahmad Aijaz ◽  
Muzamil Jallal ◽  
S. Qurat Ul Ain ◽  
Rajnee Tripathi
Keyword(s):  
Cumulative Distribution Function ◽  
Likelihood Estimation ◽  
Moment Generating Function ◽  
Rate Function ◽  
Cumulative Distribution ◽  
Parameter Distribution ◽  
Residual Function ◽  
Lorenz Curves ◽  
Method Of Maximum Likelihood ◽  
Two Parameter

This paper suggested a new two parameter distribution named as Hamza distribution. A detailed description about the properties of a suggested distribution including moments, moment generating function, deviations about mean and median, stochastic orderings, Bonferroni and Lorenz curves, Renyi entropy, order statistics, hazard rate function and mean residual function has been discussed. The behavior of a probability density function (p.d.f) and cumulative distribution function (c.d.f) have been depicted through graphs. The parameters of the distribution are estimated by the known method of maximum likelihood estimation. The performance of the established distribution have been illustrated through applications, by which we conclude that the established distribution provide better fit.

scholarly journals Inverse Power Akash Probability Distribution with Applications

2020 ◽  
pp. 1-32
Author(s):  
Samuel U. Enogwe ◽  
Happiness O. Obiora-Ilouno ◽  
Chrisogonus K. Onyekwere
Keyword(s):  
Stochastic Ordering ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Rate Function ◽  
Inverse Power ◽  
Data Sets ◽  
Unknown Parameters ◽  
Bathtub Shape ◽  
Heavy Tailed

This paper introduces an inverse power Akash distribution as a generalization of the Akash distribution to provide better fits than the Akash distribution and some of its known extensions. The fundamental properties of the proposed distribution such as the shapes of the distribution, moments, mean, variance, coefficient of variation, skewness, kurtosis, moment generating function, quantile function, Rényi entropy, stochastic ordering and the distribution of order statistics have been derived. The proposed distribution is observed to be a heavy-tailed distribution and can also be used to model data with upside-down bathtub shape for its hazard rate function. The maximum likelihood estimators of the unknown parameters of the proposed distribution have been obtained. Two numerical examples are given to demonstrate the applicability of the proposed distribution and for the two real data sets, the proposed distribution is found to be superior in its ability to sufficiently model heavy-tailed data than Akash, inverse Akash and power Akash distributions respectively.

scholarly journals A New Five Parameter Lifetime Distribution: Properties and Application

2017 ◽  
Vol 13 (3) ◽  
pp. 7205-7218
Author(s):  
Shimaa A. Dessoky ◽  
Ahmed M. T. Abd El-Bar
Keyword(s):  
Hazard Rate ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Rate Function ◽  
Lifetime Distribution ◽  
Maximum Likelihood Estimates ◽  
Hazard Rate Function ◽  
Unknown Parameters ◽  
Data Set ◽  
Present Distribution

This paper deals with a new generalization of the Weibull distribution. This distribution is called exponentiated exponentiated exponential-Weibull (EEE-W) distribution. Various structural properties of the new probabilistic model are considered, such as hazard rate function, moments, moment generating function, quantile function, skewness, kurtosis, Shannon entropy and Rényi entropy. The maximum likelihood estimates of its unknown parameters are obtained. Finally, areal data set is analyzed and it observed that the present distribution can provide a better fit than some other known distributions.

scholarly journals A Transmuted Lomax-Exponential Distribution: Properties and Applications

2019 ◽  
pp. 1-13
Author(s):  
S. Kuje ◽  
K. E. Lasisi
Keyword(s):  
Exponential Distribution ◽  
Probability Distributions ◽  
Survival Function ◽  
Real Life ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Cumulative Distribution ◽  
Method Of Maximum Likelihood ◽  
New Distribution

In this article, the Quadratic rank transmutation map proposed and studied by Shaw and Buckley [1] is used to construct and study a new distribution called the transmuted Lomax-Exponential distribution (TLED) as an extension of the Lomax-Exponential distribution recently proposed by Ieren and Kuhe [2]. Using the transmutation map, we defined the probability density function and cumulative distribution function of the transmuted Lomax-Exponential distribution. Some properties of the new distribution such as moments, moment generating function, characteristics function, quantile function, survival function, hazard function and order statistics are also studied. The estimation of the distributions’ parameters has been done using the method of maximum likelihood estimation. The performance of the proposed probability distribution is being tested in comparison with some other generalizations of Exponential distribution using a real life dataset. The results obtained show that the TLED performs better than the other probability distributions.

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