Truncated log-logistic Family of Distributions

Likelihood Method ◽

Logistic Distribution ◽

Real Dataset ◽

New Family ◽

The Family ◽

The World ◽

Family Of Distributions ◽

Better Than

Background & Aim: There are various data associated with any events in the world which need to be analyzed. In response to this, many researchers attempt to find appropriate methods that could better fit these data using new models. One of these methods is to introduce new distributions which could better describe available data. During last few years, new distributions have been extended based on existing well-known distributions. Usually, new distributions have more parameters than existing ones. This addition of parameter(s) has been proved useful in exploring tail properties and also for improving the goodness-of-fit of the family under study. Methods & Materials: A new family of distributions is introduced by using truncated log-logistic distribution. Some statistical and reliability properties of the new family are derived. Results: Four special lifetime models of the new family are investigated. We estimate the parameters by maximum likelihood method. The obtained results are validated using a real dataset and it is shown that the new distributions provide a better fit than some other known distributions. Conclusion: We have provided four new distributions. The flexibility of the proposed distributions and increased range of skewness was able to fit and capture features in one real dataset much better than some competitor distributions

Discrete Gompertz-G Family of Distributions for Over- and Under-Dispersed Data with Properties, Estimation, and Applications

Mathematics ◽

10.3390/math8030358 ◽

2020 ◽

Vol 8 (3) ◽

pp. 358 ◽

Cited By ~ 3

Author(s):

M. S. Eliwa ◽

Ziyad Ali Alhussain ◽

M. El-Morshedy

Keyword(s):

Maximum Likelihood ◽

Discrete Analogue ◽

Likelihood Method ◽

New Family ◽

Distributional Properties ◽

Reliability Characteristics ◽

Proposed Model ◽

The Family ◽

Alizadeh et al. introduced a flexible family of distributions, in the so-called Gompertz-G family. In this article, a discrete analogue of the Gompertz-G family is proposed. We also study some of its distributional properties and reliability characteristics. After introducing the general class, three special models of the new family are discussed in detail. The maximum likelihood method is used for estimating the family parameters. A simulation study is carried out to assess the performance of the family parameters. Finally, the flexibility of the new family is illustrated by means of four genuine datasets, and it is found that the proposed model provides a better fit than the competitive distributions.

The Generalized Additive Weibull-G Family of Distributions

International Journal of Statistics and Probability ◽

10.5539/ijsp.v6n5p65 ◽

2017 ◽

Vol 6 (5) ◽

pp. 65 ◽

Cited By ~ 6

Author(s):

Amal S. Hassan ◽

Saeed E. Hemeda ◽

Sudhansu S. Maiti ◽

Sukanta Pramanik

Keyword(s):

Real Data ◽

Random Variable ◽

Likelihood Method ◽

Parameter Estimates ◽

Data Sets ◽

New Family ◽

The Family ◽

Generated Family ◽

In this paper, we present a new family, depending on additive Weibull random variable as a generator, called the generalized additive Weibull generated-family (GAW-G) of distributions with two extra parameters. The proposed family involves several of the most famous classical distributions as well as the new generalized Weibull-G family which already accomplished by Cordeiro et al. (2015). Four special models are displayed. The expressions for the incomplete and ordinary moments, quantile, order statistics, mean deviations, Lorenz and Benferroni curves are derived. Maximum likelihood method of estimation is employed to obtain the parameter estimates of the family. The simulation study of the new models is conducted. The efficiency and importance of the new generated family is examined through real data sets.

The Topp Leone Kumaraswamy-G Family of Distributions with Applications to Cancer Disease Data

Journal of Biostatistics and Epidemiology ◽

10.18502/jbe.v6i1.4758 ◽

2020 ◽

Author(s):

Ibrahim Sule ◽

Sani Ibrahim Doguwa ◽

Audu Isah ◽

Haruna Muhammad Jibril

Keyword(s):

Goodness Of Fit ◽

Real Data ◽

Logistic Distribution ◽

Data Sets ◽

Medical Sciences ◽

Cancer Disease ◽

Underlying Distribution ◽

New Family ◽

The Family ◽

Background: In the last few years, statisticians have introduced new generated families of univariate distributions. These new generators are obtained by adding one or more extra shape parameters to the underlying distribution to get more flexibility in fitting data in different areas such as medical sciences, economics, finance and environmental sciences. The addition of parameter(s) has been proven useful in exploring tail properties and also for improving the goodness-of-fit of the family of distributions under study. Methods: A new three-parameter family of distributions was introduced by using the idea of T-X methodology. Some statistical properties of the new family were derived and studied. Results: A new Topp Leone Kumaraswamy-G family of distributions was introduced. Two special sub-models, that is, the Topp Leone Kumaraswamy exponential distribution and Topp Leone Kumaraswamy log-logistic distribution were investigated. Two real data sets were used to assess the flexibility of the sub-models. Conclusion: The results suggest that the two sub-models performed better than their competitors.

Inverse Lomax-Exponentiated G (IL-EG) Family of Distributions: Properties and Applications

Asian Journal of Probability and Statistics ◽

10.9734/ajpas/2020/v9i430234 ◽

2020 ◽

pp. 48-64

Author(s):

Jamilu Yunusa Falgore ◽

Sani Ibrahim Doguwa

Keyword(s):

Maximum Likelihood ◽

Moment Generating Function ◽

Maximum Likelihood Estimates ◽

Likelihood Method ◽

Data Sets ◽

Baseline Model ◽

New Family ◽

Family Of Distributions ◽

Better Than

A new generator of continuous distributions called the Inverse Lomax-Exponentiated G family, which has three extra positive parameters is proposed. The structural properties of the new family that holds for any continuous baseline model including explicit density function expressions, moments, inequality measurements, moment generating function, reliability functions, Renyi and Shanon entropies, and distribution of order statistics are derived. A Monte Carlo simulation to test the efficiency of the maximum likelihood estimates is conducted. The application of the new sub-model to the two data sets using the maximum likelihood method indicates that the new model is better than the existing competitors.

Modified generalized marshall-olkin family of distributions

International Journal of Advanced Statistics and Probability ◽

10.14419/ijasp.v7i1.28916 ◽

2019 ◽

Vol 7 (1) ◽

pp. 18

Author(s):

Muhammad Aslam ◽

Zawar Hussain ◽

Zahid Asghar

Keyword(s):

Maximum Likelihood ◽

Goodness Of Fit ◽

Likelihood Estimation ◽

Likelihood Method ◽

Model Parameters ◽

Data Sets ◽

Goodness Of Fit Tests ◽

New Family ◽

In this article, we propose a new family of distributions using the T-X family named as modified generalized Marshall-Olkin family of distributions. Comprehensive mathematical and statistical properties of this family of distributions are provided. The model parameters are estimated by maximum likelihood method. The maximum likelihood estimation under Type-II censoring is also discussed. Two lifetime data sets are used to show the suitability and applicability of the new family of distributions. For comparison purposes, different goodness of fit tests are used.

Pseudo-Lindley Family of Distributions and its Properties

Asian Research Journal of Mathematics ◽

10.9734/arjom/2021/v17i530298 ◽

2021 ◽

pp. 35-49

Author(s):

U. U. Uwadi ◽

E. E. Nwezza

Keyword(s):

Hazard Rate ◽

Quantile Function ◽

Rate Function ◽

Likelihood Method ◽

Parameter Estimates ◽

New Family ◽

The Family ◽

Renyi’S Entropy ◽

In this study, we proposed a family of distribution called the Pseudo Lindley family of distributions. The limiting behaviors of the density and hazard rate function of the new family are examined. Statistical properties of the proposed family of distributions derived include quantile function, moments, order statistics, and Renyi’s entropy. The maximum likelihood method was employed in obtaining the parameter estimates of the Pseudo Lindley family of distribution. Bivariate extension of the proposed family is discussed. Some special members of the family are obtained. The shape of the density function of special members could be unimodal, bathtub shaped, increasing and decreasing.

Truncated Cauchy Power Odd Fréchet-G Family of Distributions: Theory and Applications

Complexity ◽

10.1155/2021/4256945 ◽

2021 ◽

Vol 2021 ◽

pp. 1-9

Author(s):

M. Shrahili ◽

I. Elbatal

Keyword(s):

Exponential Model ◽

Likelihood Method ◽

Mean Deviation ◽

Model Parameters ◽

Lorenz Curves ◽

New Family ◽

The Family ◽

Real World Datasets ◽

The truncated Cauchy power odd Fréchet-G family of distributions is presented in this article. This family’s unique models are launched. Statistical properties of the new family are proposed, such as density function expansion, moments, incomplete moments, mean deviation, Bonferroni and Lorenz curves, and entropy. We investigate the maximum likelihood method for predicting model parameters of the new family. Two real-world datasets are used to show the importance and flexibility of the new family by using the truncated Cauchy power odd Fréchet exponential model as example of the family and compare it with some known models, and this model proves the importance and the flexibility for the new family.

The extended odd family of probability distributions with practice to a submodel

Filomat ◽

10.2298/fil1912855b ◽

2019 ◽

Vol 33 (12) ◽

pp. 3855-3867 ◽

Cited By ~ 2

Author(s):

Hassan Bakouch ◽

Christophe Chesneau ◽

Muhammad Khan

Keyword(s):

Heavy Tails ◽

Probability Distributions ◽

Likelihood Method ◽

Tuning Parameter ◽

Data Sets ◽

New Family ◽

Rate Functions ◽

Special Case ◽

In this paper, we introduce a new family of distributions extending the odd family of distributions. A new tuning parameter is introduced, with some connections to the well-known transmuted transformation. Some mathematical results are obtained, including moments, generating function and order statistics. Then, we study a special case dealing with the standard loglogistic distribution and the modifiedWeibull distribution. Its main features are to have densities with flexible shapes where skewness, kurtosis, heavy tails and modality can be observed, and increasing-decreasing-increasing, unimodal and bathtub shaped hazard rate functions. Estimation of the related parameters is investigated by the maximum likelihood method. We illustrate the usefulness of our extended odd family of distributions with applications to two practical data sets.

A New-Flexible Generated Family of Distributions Based on Half-Logistic Distribution

Journal of Computational and Theoretical Nanoscience ◽

10.1166/jctn.2020.9332 ◽

2020 ◽

Vol 17 (11) ◽

pp. 4813-4818

Author(s):

Sanaa Al-Marzouki ◽

Sharifah Alrajhi

Keyword(s):

Logistic Model ◽

Real Data ◽

Likelihood Method ◽

Logistic Distribution ◽

Data Set ◽

New Family ◽

Probability Weighted Moment ◽

The Subject ◽

Generated Family ◽

We proposed a new family of distributions from a half logistic model called the generalized odd half logistic family. We expressed its density function as a linear combination of exponentiated densities. We calculate some statistical properties as the moments, probability weighted moment, quantile and order statistics. Two new special models are mentioned. We study the estimation of the parameters for the odd generalized half logistic exponential and the odd generalized half logistic Rayleigh models by using maximum likelihood method. One real data set is assesed to illustrate the usefulness of the subject family.

Extended Odd Fréchet-G Family of Distributions

Journal of Probability and Statistics ◽

10.1155/2018/2931326 ◽

2018 ◽

Vol 2018 ◽

pp. 1-12 ◽

Cited By ~ 6

Author(s):

Suleman Nasiru

Keyword(s):

Real Data ◽

Likelihood Method ◽

Data Sets ◽

Data Set ◽

New Class ◽

New Family ◽

Rate Functions ◽

The Given ◽

The need to develop generalizations of existing statistical distributions to make them more flexible in modeling real data sets is vital in parametric statistical modeling and inference. Thus, this study develops a new class of distributions called the extended odd Fréchet family of distributions for modifying existing standard distributions. Two special models named the extended odd Fréchet Nadarajah-Haghighi and extended odd Fréchet Weibull distributions are proposed using the developed family. The densities and the hazard rate functions of the two special distributions exhibit different kinds of monotonic and nonmonotonic shapes. The maximum likelihood method is used to develop estimators for the parameters of the new class of distributions. The application of the special distributions is illustrated by means of a real data set. The results revealed that the special distributions developed from the new family can provide reasonable parametric fit to the given data set compared to other existing distributions.