scholarly journals The Generalized DUS Transformed Log-Normal Distribution and Its Applications to Cancer and Heart Transplant Datasets

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3113
Author(s):  
Muhammed Rasheed Irshad ◽  
Christophe Chesneau ◽  
Soman Latha Nitin ◽  
Damodaran Santhamani Shibu ◽  
Radhakumari Maya
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Hazard Rate ◽  
Rate Function ◽  
Biological Data ◽  
Hazard Rate Function ◽  
Bayesian Techniques ◽  
Log Normal ◽  
Log Normal Distribution ◽  
New Distribution

Many studies have underlined the importance of the log-normal distribution in the modeling of phenomena occurring in biology. With this in mind, in this article we offer a new and motivated transformed version of the log-normal distribution, primarily for use with biological data. The hazard rate function, quantile function, and several other significant aspects of the new distribution are investigated. In particular, we show that the hazard rate function has increasing, decreasing, bathtub, and upside-down bathtub shapes. The maximum likelihood and Bayesian techniques are both used to estimate unknown parameters. Based on the proposed distribution, we also present a parametric regression model and a Bayesian regression approach. As an assessment of the longstanding performance, simulation studies based on maximum likelihood and Bayesian techniques of estimation procedures are also conducted. Two real datasets are used to demonstrate the applicability of the new distribution. The efficiency of the third parameter in the new model is tested by utilizing the likelihood ratio test. Furthermore, the parametric bootstrap approach is used to determine the effectiveness of the suggested model for the datasets.

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.

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

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 The Topp-Leone odd log-logistic Gumbel Distribution: Properties and Applications

2020 ◽  
Vol 9 (2) ◽  
pp. 288-310
Author(s):  
Fazlollah Lak ◽  
Morad Alizadeh ◽  
Hamid Karamikabir
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Hazard Rate ◽  
Gumbel Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Rate Function ◽  
Model Parameters ◽  
Data Sets ◽  
Hazard Rate Function

In this article, the Topp-Leone odd log-logistic Gumbel (TLOLL-Gumbel) family of distribution have beenstudied. This family, contains the very flexible skewed density function. We study many aspects of the new model like hazard rate function, asymptotics, useful expansions, moments, generating Function, R´enyi entropy and order statistics. We discuss maximum likelihood estimation of the model parameters. Further, we study flexibility of the proposed family are illustrated of two real data sets.

scholarly journals The beta Gumbel distribution

2004 ◽  
Vol 2004 (4) ◽  
pp. 323-332 ◽  
Author(s):  
Saralees Nadarajah ◽  
Samuel Kotz
Keyword(s):  
Hazard Rate ◽  
Gumbel Distribution ◽  
Random Variable ◽  
Rate Function ◽  
Comprehensive Treatment ◽  
Hazard Rate Function ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood ◽  
New Distribution ◽  
Skewness And Kurtosis

The Gumbel distribution is perhaps the most widely applied statistical distribution for problems in engineering. In this paper, we introduce a generalization—referred to as the beta Gumbel distribution—generated from the logit of a beta random variable. We provide a comprehensive treatment of the mathematical properties of this new distribution. We derive the analytical shapes of the corresponding probability density function and the hazard rate function and provide graphical illustrations. We calculate expressions for thenth moment and the asymptotic distribution of the extreme order statistics. We investigate the variation of the skewness and kurtosis measures. We also discuss estimation by the method of maximum likelihood. We hope that this generalization will attract wider applicability in engineering.

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).

On log-bimodal alpha-power distributions with application to nickel contents and erosion data

2021 ◽  
Vol 71 (6) ◽  
pp. 1565-1580
Author(s):  
Hugo S. Salinas ◽  
Guillermo Martínez-Flórez ◽  
Artur J. Lemonte ◽  
Heleno Bolfarine
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Fisher Information ◽  
Power Distribution ◽  
Information Matrix ◽  
Likelihood Method ◽  
Model Parameters ◽  
Alpha Power ◽  
Log Normal ◽  
Log Normal Distribution

Abstract In this paper, we present a new parametric class of distributions based on the log-alpha-power distribution, which contains the well-known log-normal distribution as a special case. This new family is useful to deal with unimodal as well as bimodal data with asymmetry and kurtosis coefficients ranging far from that expected based on the log-normal distribution. The usual approach is considered to perform inferences, and the traditional maximum likelihood method is employed to estimate the unknown parameters. Monte Carlo simulation results indicate that the maximum likelihood approach is quite effective to estimate the model parameters. We also derive the observed and expected Fisher information matrices. As a byproduct of such study, it is shown that the Fisher information matrix is nonsingular throughout the sample space. Empirical applications of the proposed family of distributions to real data are provided for illustrative purposes.

scholarly journals On Extended Quadratic Hazard Rate Distribution: Development, Properties, Characterizations and Applications

2018 ◽  
Vol 33 (1) ◽  
pp. 45-60 ◽  
Author(s):  
Fiaz Ahmad Bhatti ◽  
G. G. Hamedani ◽  
Wenhui Sheng ◽  
Munir Ahmad
Keyword(s):  
Maximum Likelihood ◽  
Hazard Rate ◽  
Goodness Of Fit ◽  
Maximum Likelihood Method ◽  
Rate Function ◽  
Likelihood Method ◽  
Mixture Distributions ◽  
Hazard Rate Function ◽  
Reliability Measures ◽  
Stochastic Orderings

Abstract In this paper, we propose a flexible extended quadratic hazard rate (EQHR) distribution with increasing, decreasing, bathtub and upside-down bathtub hazard rate function. The EQHR density is arc, right-skewed and symmetrical shaped. This distribution is also obtained from compounding mixture distributions. Stochastic orderings, descriptive measures on the basis of quantiles, order statistics and reliability measures are theoretically established. Characterizations of the EQHR distribution are studied via different techniques. Parameters of the EQHR distribution are estimated using the maximum likelihood method. Goodness of fit of this distribution through different methods is studied.

Sign in / Sign up

Export Citation Format

Share Document