The Odd Log-Logistic Log-Normal Distribution with Theory and Applications

2018 ◽  
Vol 10 (04) ◽  
pp. 1850009 ◽  
Author(s):  
Gamze Ozel ◽  
Emrah Altun ◽  
Morad Alizadeh ◽  
Mahdieh Mozafari
Keyword(s):  
Normal Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Procedure ◽  
Quantile Function ◽  
Logistic Distribution ◽  
Unknown Parameters ◽  
Heavy Tailed ◽  
Log Normal ◽  
Log Normal Distribution

In this paper, a new heavy-tailed distribution is used to model data with a strong right tail, as often occuring in practical situations. The proposed distribution is derived from the log-normal distribution, by using odd log-logistic distribution. Statistical properties of this distribution, including hazard function, moments, quantile function, and asymptotics, are derived. The unknown parameters are estimated by the maximum likelihood estimation procedure. For different parameter settings and sample sizes, a simulation study is performed and the performance of the new distribution is compared to beta log-normal. The new lifetime model can be very useful and its superiority is illustrated by means of two real data sets.

scholarly journals The New Novel Discrete Distribution with Application on COVID-19 Mortality Numbers in Kingdom of Saudi Arabia and Latvia

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
M. Nagy ◽  
Ehab M. Almetwally ◽  
Ahmed M. Gemeay ◽  
Heba S. Mohammed ◽  
Taghreed M. Jawa ◽  
...  
Keyword(s):  
Saudi Arabia ◽  
Statistical Model ◽  
Discrete Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Linear Representation ◽  
Quantile Function ◽  
Mortality Data ◽  
Unknown Parameters ◽  
New Novel

This paper aims to introduce a superior discrete statistical model for the coronavirus disease 2019 (COVID-19) mortality numbers in Saudi Arabia and Latvia. We introduced an optimal and superior statistical model to provide optimal modeling for the death numbers due to the COVID-19 infections. This new statistical model possesses three parameters. This model is formulated by combining both the exponential distribution and extended odd Weibull family to formulate the discrete extended odd Weibull exponential (DEOWE) distribution. We introduced some of statistical properties for the new distribution, such as linear representation and quantile function. The maximum likelihood estimation (MLE) method is applied to estimate the unknown parameters of the DEOWE distribution. Also, we have used three datasets as an application on the COVID-19 mortality data in Saudi Arabia and Latvia. These three real data examples were used for introducing the importance of our distribution for fitting and modeling this kind of discrete data. Also, we provide a graphical plot for the data to ensure our results.

scholarly journals The Exponentiated Lindley Geometric Distribution with Applications

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 510
Author(s):  
Bo Peng ◽  
Zhengqiu Xu ◽  
Min Wang
Keyword(s):  
Maximum Likelihood ◽  
Geometric Distribution ◽  
Residual Life ◽  
Information Matrix ◽  
Expectation Maximization Algorithm ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Maximum Likelihood Estimates ◽  
Unknown Parameters

We introduce a new three-parameter lifetime distribution, the exponentiated Lindley geometric distribution, which exhibits increasing, decreasing, unimodal, and bathtub shaped hazard rates. We provide statistical properties of the new distribution, including shape of the probability density function, hazard rate function, quantile function, order statistics, moments, residual life function, mean deviations, Bonferroni and Lorenz curves, and entropies. We use maximum likelihood estimation of the unknown parameters, and an Expectation-Maximization algorithm is also developed to find the maximum likelihood estimates. The Fisher information matrix is provided to construct the asymptotic confidence intervals. Finally, two real-data examples are analyzed for illustrative purposes.

scholarly journals Two symmetric and computationally efficient Gini correlations

2020 ◽  
Vol 8 (1) ◽  
pp. 373-395
Author(s):  
Courtney Vanderford ◽  
Yongli Sang ◽  
Xin Dang
Keyword(s):  
Influence Function ◽  
Random Variables ◽  
Real Data ◽  
Computationally Efficient ◽  
Gini Correlation ◽  
Heavy Tailed Distributions ◽  
Data Application ◽  
Heavy Tailed ◽  
Log Normal ◽  
Log Normal Distribution

AbstractStandard Gini correlation plays an important role in measuring the dependence between random variables with heavy-tailed distributions. It is based on the covariance between one variable and the rank of the other. Hence for each pair of random variables, there are two Gini correlations and they are not equal in general, which brings a substantial difficulty in interpretation. Recently, Sang et al (2016) proposed a symmetric Gini correlation based on the joint spatial rank function with a computation cost of O(n2) where n is the sample size. In this paper, we study two symmetric and computationally efficient Gini correlations with the computational complexity of O(n log n). The properties of the new symmetric Gini correlations are explored. The influence function approach is utilized to study the robustness and the asymptotic behavior of these correlations. The asymptotic relative efficiencies are considered to compare several popular correlations under symmetric distributions with different tail-heaviness as well as an asymmetric log-normal distribution. Simulation and real data application are conducted to demonstrate the desirable performance of the two new symmetric Gini correlations.

scholarly journals Statistical analysis based on quaternion normal random variables

1985 ◽  
Vol 4 (3) ◽  
pp. 120-127 ◽  
Author(s):  
H. M. Rautenbach ◽  
J. J. J. Roux
Keyword(s):  
Statistical Analysis ◽  
Maximum Likelihood ◽  
Probability Density Function ◽  
Maximum Likelihood Estimation ◽  
Normal Distribution ◽  
Probability Density ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Unknown Parameters ◽  
Quaternion Case

The quaternion normal distribution is derived and a number of characteristics are highlighted. The maximum likelihood estimation procedure in the quaternion case is examined and the conclusion is reached that the estimation procedure is simplified if the unknown parameters of the associated real probability density function are estimated. The quaternion estimator is then obtained by regarding these estimators as the components of the quaternion estimator. By means of a example attention is given to a test criterium which can be used in the quaternion model.

scholarly journals The accumulative law and its probability model: an extension of the Pareto distribution and the log-normal distribution

2020 ◽  
Vol 476 (2237) ◽  
pp. 20200019 ◽  
Author(s):  
Minyu Feng ◽  
Liang-Jian Deng ◽  
Feng Chen ◽  
Matjaž Perc ◽  
Jürgen Kurths
Keyword(s):  
Social Sciences ◽  
Complex Networks ◽  
Normal Distribution ◽  
Complex Network ◽  
Pareto Distribution ◽  
Probability Model ◽  
Real Data ◽  
The Past ◽  
Log Normal ◽  
Log Normal Distribution

The divergence between the Pareto distribution and the log-normal distribution has been observed persistently over the past couple of decades in complex network research, economics, and social sciences. To address this, we here propose an approach termed as the accumulative law and its related probability model. We show that the resulting accumulative distribution has properties that are akin to both the Pareto distribution and the log-normal distribution, which leads to a broad range of applications in modelling and fitting real data. We present all the details of the accumulative law, describe the properties of the distribution, as well as the allocation and the accumulation of variables. We also show how the proposed accumulative law can be applied to generate complex networks, to describe the accumulation of personal wealth, and to explain the scaling of internet traffic across different domains.

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.

Estimation of thermal time model parameters for seed germination in 15 species: the importance of distribution function

2021 ◽  
pp. 1-8
Author(s):  
Dali Chen ◽  
Xianglai Chen ◽  
Jingjing Wang ◽  
Zuxin Zhang ◽  
Yan Wang ◽  
...  
Keyword(s):  
Distribution Function ◽  
Seed Germination ◽  
Normal Distribution ◽  
Distribution Functions ◽  
Thermal Time ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Time Model ◽  
Log Normal ◽  
Log Normal Distribution

Abstract Thermal time models have been widely applied to predict temperature requirements for seed germination. Generally, a log-normal distribution for thermal time [θT(g)] is used in such models at suboptimal temperatures to examine the variation in time to germination arising from variation in θT(g) within a seed population. Recently, additional distribution functions have been used in thermal time models to predict seed germination dynamics. However, the most suitable kind of the distribution function to use in thermal time models, especially at suboptimal temperatures, has not been determined. Five distributions (log-normal, Gumbel, logistic, Weibull and log-logistic) were used in thermal time models over a range of temperatures to fit the germination data for 15 species. The results showed that a more flexible model with the log-logistic distribution, rather than the log-normal distribution, provided the best explanation of θT(g) variation in 13 species at suboptimal temperatures. Thus, at least at suboptimal temperatures, the log-logistic distribution is an appropriate candidate among the five distributions used in this study. Therefore, the distribution of parameters [θT(g)] should be considered when using thermal time models to prevent large deviations; furthermore, an appropriate equation should be selected before using such a model to make predictions.

scholarly journals Logit Truncated-Exponential Skew-Logistic Distribution with Properties and Applications

Modelling ◽  
2021 ◽  
Vol 2 (4) ◽  
pp. 776-794
Author(s):  
Liyuan Pang ◽  
Weizhong Tian ◽  
Tingting Tong ◽  
Xiangfei Chen
Keyword(s):  
Residual Life ◽  
Real Data ◽  
Interval Data ◽  
Quantile Function ◽  
Likelihood Method ◽  
Logistic Distribution ◽  
Mean Deviation ◽  
Mean Residual Life ◽  
Unknown Parameters ◽  
Bounded Interval

In recent years, bounded distributions have attracted extensive attention. At the same time, various areas involve bounded interval data, such as proportion and ratio. In this paper, we propose a new bounded model, named logistic Truncated exponential skew logistic distribution. Some basic statistical properties of the proposed distribution are studied, including moments, mean residual life function, Renyi entropy, mean deviation, order statistics, exponential family, and quantile function. The maximum likelihood method is used to estimate the unknown parameters of the proposed distribution. More importantly, the applications to three real data sets mainly from the field of engineering science prove that the logistic Truncated exponential skew logistic distribution fits better than other bounded distributions.

scholarly journals Kumaraswamy Distribution Based on Alpha Power Transformation Methods

2021 ◽  
pp. 14-29
Author(s):  
H. E. Hozaien ◽  
G. R. AL Dayian ◽  
A. A. EL-Helbawy
Keyword(s):  
Residual Life ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Mean Residual Life ◽  
Alpha Power ◽  
Unknown Parameters ◽  
Data Set ◽  
Kumaraswamy Distribution

In this paper, the alpha power Kumaraswamy distribution, new alpha power transformed Kumaraswamy distribution and new extended alpha power transformed Kumaraswamy distribution are presented. Some statistical properties of the three distributions are derived including quantile function, moments and moment generating function, mean residual life and order statistics. Estimation of the unknown parameters based on maximum likelihood estimation are obtained. A simulation study is carried out. Finally, a real data set is applied.

Sign in / Sign up

Export Citation Format

Share Document