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 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 A Study on Properties and Applications of a Lomax Gompertz-Makeham Distribution

2019 ◽  
pp. 1-27
Author(s):  
Innocent Boyle Eraikhuemen ◽  
Terna Godfrey Ieren ◽  
Tajan Mashingil Mabur ◽  
Mohammed Sa’ad ◽  
Samson Kuje ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Probability Distributions ◽  
Real Life ◽  
Likelihood Estimation ◽  
The Other ◽  
Unknown Parameters ◽  
Method Of Maximum Likelihood ◽  
Compound Model ◽  
New Distribution

The article presents an extension of the Gompertz-Makeham distribution using the Lomax generator of probability distributions. This generalization of the Gompertz-Makeham distribution provides a more skewed and flexible compound model called Lomax Gompertz-Makeham distribution. The paper derives and discusses some Mathematical and Statistical properties of the new distribution. The unknown parameters of the new model are estimated via the method of maximum likelihood estimation. In conclusion, the new distribution is applied to two real life datasets together with two other related models to check its flexibility or performance and the results indicate that the proposed extension is more flexible compared to the other two distributions considered in the paper based on the two datasets used.

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.

scholarly journals The Transmuted Inverted Nadarajah-Haghighi Distribution With an Application to Lifetime Data

2021 ◽  
pp. 451-466
Author(s):  
Aliyeh Toumaj ◽  
S.M.T.K. MirMostafaee ◽  
G.G. Hamedani
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Interval Estimation ◽  
Likelihood Estimation ◽  
Lifetime Distribution ◽  
Lifetime Data ◽  
Unknown Parameters ◽  
Failure Data ◽  
Mathematical Properties ◽  
New Distribution

In this paper, we propose a new lifetime distribution. We discuss several mathematical properties of the new distribu- tion. Certain characterizations of the new distribution are provided. We study the maximum likelihood estimation and asymptotic interval estimation of the unknown parameters. A simulation study, as well as an application of the new distribution to failure data, are also presented. We end the paper with a number of remarks.

scholarly journals Half Logistic Exponential Extension Distribution with Properties and Applications

2020 ◽  
Vol 9 (3) ◽  
pp. 506-512
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Hazard Rate ◽  
Goodness Of Fit ◽  
Likelihood Estimation ◽  
Real Data ◽  
Model Parameters ◽  
Type I ◽  
Proposed Model ◽  
New Distribution

In this article, we have introduced a new distribution based on type I half logistic-G family and exponential extension as a base distribution known as Half Logistic Exponential Extension (HLEE) distribution. The statistical properties of this model are also explored, such as the behavior of probability density, hazard rate, and quantile functions are investigated. The Maximum likelihood estimation (MLE) method is used to estimate model parameters. For the potentiality of the proposed model we have compared the goodness of fit with some others models. We have proven the importance and flexibility of the new distribution in modeling with real data applications empirically.

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).

scholarly journals Statistical Properties and Different Methods of Estimation for Type I Half Logistic Inverted Kumaraswamy Distribution

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 1002 ◽  
Author(s):  
Ramadan A. ZeinEldin ◽  
Christophe Chesneau ◽  
Farrukh Jamal ◽  
Mohammed Elgarhy
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Least Squares ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Estimation Methods ◽  
Type I ◽  
Kumaraswamy Distribution ◽  
Method Of Maximum Likelihood ◽  
New Distribution

In this paper, we introduce and study a new three-parameter lifetime distribution constructed from the so-called type I half-logistic-G family and the inverted Kumaraswamy distribution, naturally called the type I half-logistic inverted Kumaraswamy distribution. The main feature of this new distribution is to add a new tuning parameter to the inverted Kumaraswamy (according to the type I half-logistic structure), with the aim to increase the flexibility of the related inverted Kumaraswamy model and thus offering more precise diagnostics in data analyses. The new distribution is discussed in detail, exhibiting various mathematical and statistical properties, with related graphics and numerical results. An exhaustive simulation was conducted to investigate the estimation of the model parameters via several well-established methods, including the method of maximum likelihood estimation, methods of least squares and weighted least squares estimation, and method of Cramer-von Mises minimum distance estimation, showing their numerical efficiency. Finally, by considering the method of maximum likelihood estimation, we apply the new model to fit two practical data sets. In this regards, it is proved to be better than recent models, also derived to the inverted Kumaraswamy distribution.

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