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 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 A New Generalized Transmuted Inverse Exponential Distribution: Properties and Application

2018 ◽  
pp. 1-13
Author(s):  
Uchenna U. Uwadi ◽  
Elebe E. Nwaezza
Keyword(s):  
Exponential Distribution ◽  
Real Life ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Maximum Likelihood Estimates ◽  
Data Set ◽  
Real Life Data ◽  
Proposed Model ◽  
Inverse Exponential Distribution ◽  
The Moment

In this study, we proposed a new generalised transmuted inverse exponential distribution with three parameters and have transmuted inverse exponential and inverse exponential distributions as sub models. The hazard function of the distribution is nonmonotonic, unimodal and inverted bathtub shaped making it suitable for modelling lifetime data. We derived the moment, moment generating function, quantile function, maximum likelihood estimates of the parameters, Renyi entropy and order statistics of the distribution. A real life data set is used to illustrate the usefulness of the proposed model.     

scholarly journals THE NEW WEIGHTED INVERSE RAYLEIGH DISTRIBUTION AND ITS APPLICATION

2019 ◽  
pp. 511
Author(s):  
Demet Aydın
Keyword(s):  
Maximum Likelihood ◽  
Moment Generating Function ◽  
Rayleigh Distribution ◽  
Maximum Likelihood Estimates ◽  
Weight Functions ◽  
Unknown Parameters ◽  
Weighted Version ◽  
Data Set ◽  
Mean Wind Speed ◽  
Rate Functions

In this study, a new weighted version of the inverse Rayleigh distribution based on two different weight functions is introduced. Some statistical and reliability properties of the introduced distribution including the moments, moment generating function, entropy measures (i.e., Shannon and R´enyi) and survival and hazard rate functions are derived. The maximum likelihood estimators of the unknown parameters cannot be obtained in explicit forms. So, a numerical method has been required to compute maximum likelihood estimates. Finally, the daily mean wind speed data set has been analysed to show the usability of the new weighted inverse Rayleigh distribution.

Discrete Distribution for the Stochastic Range of a Wiener Process and Its Properties

2019 ◽  
Vol 18 (04) ◽  
pp. 1950024 ◽  
Author(s):  
Mohamed Abd Allah El-Hadidy
Keyword(s):  
Order Statistics ◽  
Wiener Process ◽  
Hazard Rate ◽  
Discrete Distribution ◽  
Rate Function ◽  
Strength Parameter ◽  
Hazard Rate Function ◽  
Data Set ◽  
Basic Properties ◽  
Distributional Properties

We introduce the discrete distribution of a Wiener process range (DDWPR). Rather than finding some basic distributional properties including hazard rate function, moments, stress-strength parameter and order statistics of this distribution, this paper studies some basic properties of the truncated version of this distribution. The effectiveness of this distribution is established using a data set.

scholarly journals THE BETA-WEIBULL DISTRIBUTION ON THE LATTICE OF INTEGERS

2016 ◽  
Vol 39 (1) ◽  
pp. 40 ◽  
Author(s):  
Vahid Nekoukhou ◽  
Hamid Bidram ◽  
Rasool Roozegar
Keyword(s):  
Weibull Distribution ◽  
Hazard Rate ◽  
Real Data ◽  
Rate Function ◽  
Discrete Analog ◽  
Discrete Distributions ◽  
Hazard Rate Function ◽  
Data Set ◽  
Beta Weibull Distribution ◽  
New Distribution

In this paper, a discrete analog of the beta-Weibull distribution is studied. This new distribution contains several discrete distributions as special sub-models. Some distributional and moment properties of the discrete beta-Weibull distribution as well as its order statistics are discussed. We will show that the hazard rate function of the new model can be increasing, decreasing, bathtub-shaped and upside-down bathtub. Estimation of the parameters is illustrated and the model with a real data set is also examined.

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 The Lambert-F Distributions Class: An Alternative Family for Positive Data Analysis

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1398
Author(s):  
Yuri A. Iriarte ◽  
Mário de Castro ◽  
Héctor W. Gómez
Keyword(s):  
Hazard Rate ◽  
Quantile Function ◽  
Rate Function ◽  
Lambert W Function ◽  
Hazard Rate Function ◽  
Likelihood Methods ◽  
Baseline Hazard ◽  
New Class ◽  
Maximum Likelihood Methods ◽  
F Distribution

In this article, we introduce a new probability distribution generator called the Lambert-F generator. For any continuous baseline distribution F, with positive support, the corresponding Lambert-F version is generated by using the new generator. The result is a new class of distributions with one extra parameter that generalizes the baseline distribution and whose quantile function can be expressed in closed form in terms of the Lambert W function. The hazard rate function of a Lambert-F distribution corresponds to a modification of the baseline hazard rate function, greatly increasing or decreasing the baseline hazard rate for earlier times. Herein, we study the main structural properties of the new class of distributions. Special attention is given to two particular cases that can be understood as two-parameter extensions of the well-known exponential and Rayleigh distributions. We discuss parameter estimation for the proposed models considering the moments and maximum likelihood methods. Finally, two applications were developed to illustrate the usefulness of the proposed distributions in the analysis of data from different real settings.

scholarly journals A generalized beta function and associated probability density

2002 ◽  
Vol 30 (8) ◽  
pp. 467-478 ◽  
Author(s):  
Y. Ben Nakhi ◽  
S. L. Kalla
Keyword(s):  
Probability Density ◽  
Hazard Rate ◽  
Beta Function ◽  
Moment Generating Function ◽  
Residue Function ◽  
Rate Function ◽  
Hazard Rate Function ◽  
Scale Parameters ◽  
Special Cases ◽  
Basic Functions

We introduce and establish some properties of a generalized form of the beta function. Corresponding generalized incomplete beta functions are also defined. Moreover, we define a new probability density function (pdf) involving this new generalized beta function. Some basic functions associated with the pdf, such as moment generating function, mean residue function, and hazard rate function are derived. Some special cases are mentioned. Some figures for pdf, hazard rate function, and mean residue life function are given. These figures reflect the role of shape and scale parameters.

Transmuted Erlang-Truncated Exponential Distribution

2016 ◽  
Vol 31 (2) ◽  
Author(s):  
Idika E. Okorie ◽  
Anthony C. Akpanta ◽  
Johnson Ohakwe
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Hazard Rate ◽  
Likelihood Estimation ◽  
Rate Function ◽  
Lifetime Distribution ◽  
Hazard Rate Function ◽  
Method Of Maximum Likelihood ◽  
Two Parameter ◽  
New Distribution

AbstractThis article introduces a new lifetime distribution called the transmuted Erlang-truncated exponential (TETE) distribution. This new distribution generalizes the two parameter Erlang-truncated exponential (ETE) distribution. Closed form expressions for some of its distributional and reliability properties are provided. The method of maximum likelihood estimation was proposed for estimating the parameters of the TETE distribution. The hazard rate function of the TETE distribution can be constant, increasing or decreasing depending on the value of the transmutation parameter

Exponentiated–Exponential Logistic Distribution: Some Properties and Application

2020 ◽  
Vol 9 (1) ◽  
pp. 100-108
Author(s):  
Laxmi Prasad Sapkota
Keyword(s):  
Hazard Rate ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Rate Function ◽  
Logistic Distribution ◽  
Hazard Rate Function ◽  
Density Plot ◽  
Mathematical Properties ◽  
And Behavior ◽  
New Distribution

This study proposes new distribution which is generated from exponentiated-exponential-X family of distribution. It is explored various shape and behavior of the observed distribution through probability density plot, hazard rate function and quantile function. Further we have investigated some mathematical properties, estimation of the parameters and associated confidence interval using maximum likelihood estimation (MLE) method of the exponentiatedexponential-logistic distribution (EELD).

Sign in / Sign up

Export Citation Format

Share Document