The Unit-Logistic Distribution: Different Methods of Estimation

Abstract

This paper addresses the different methods of estimation of the unknown parameters of a two-parameter unit-logistic distribution from the frequentist point of view. We briefly describe different approaches, namely, maximum likelihood estimators, percentile based estimators, least squares estimators, maximum product of spacings estimators, methods of minimum distances: Cramér-von Mises, Anderson-Darling and four variants of Anderson-Darling. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. The performances of the estimators have been compared in terms of their relative bias, root mean squared error, average absolute difference between the theoretical and empirical estimate of the distribution functions and the maximum absolute difference between the theoretical and empirical distribution functions using simulated samples. Also, for each method of estimation, we consider the interval estimation using the Bootstrap confidence interval and calculate the coverage probability and the average width of the Bootstrap confidence intervals. Finally, two real data sets have been analyzed for illustrative purposes.

Modeling Proportion Data with Inflation by Using a Power-Skew-Normal/Logit Mixture Model

“…, δ 1r ) are vectors of unknown parameters associated with the covariate vectors z (0) and z (1) , respectively. For the continuous part, we continue assuming a truncated centered unit-PSN model, with parameters (δ, σ, λ, α) , defined in (14). One can show that the log-likelihood function for the parameters vector ϕ = (δ (0) , δ (1) , δ , σ, λ, α) , given z (0) , z, z (1) , and Y, can be written in the form…”

“…Among the most recent works, we emphasize Ospina and Ferrari [6,7], Bayes et al [8] and Martínez-Flórez et al [9,10] who have presented extensions of the works mentioned above, some of them by incorporating a set of covariates to the model. Other works in this same area are those of Mazucheli et al [11][12][13] and Menezes et al [14], which extend the Birbaum-Saunders, gamma, Weibull, and logistic models, respectively, to situations of models able to fit datasets whose variables are on a unity interval. These families have proven to be a good alternative to the beta model of Ferrari and Cribari-Neto [4] and the Kumaraswamy distribution by [15].…”

A Unit Probabilistic Model for Proportion and Asymmetric Data: Properties and Estimation Techniques with Application to Model Data from SC16 and P3 Algorithms

“…us, the researchers proposed and studied various unit distributions. Among the most useful unit distributions, there are the Johnson distribution [2], Topp-Leone distribution [3], unit-gamma distribution [4], Kumaraswamy distribution [5], log-Lindley distribution [6], unit-logistic distribution [7], unit-Birnbaum-Saunders distribution [8], log-xgamma distribution [9], unit-Lindley distribution [10], unit-Gompertz distribution [11], unit-inverse Gaussian distribution [12], unit-Bur III distribution [13], log-weighted exponential distribution [14], unit-Weibull distribution [15], unit-Modified Burr III distribution [16], unit-Rayleigh distribution [17], Frechet power function distribution [18], and unit-Burr XIII distribution [19].…”

Unit Nadarajah and Haghighi Distribution: Properties and Applications in Quality Control

“…For example, Mazucheli et al [1] introduced the unit-Weibull distribution and showed its flexibility over the beta distribution. Similarly, the unit-gamma distribution [2], unit logistic distribution [3], unit Lindley distribution [4], unit Gompertz distribution [5], Topp-Leone generated distributions [6], reflected generalized Topp-Leone power series distribution [7], etc., are introduced to deal proportion data.…”

“…time-between-events monitoring in a multistage manufacturing system", The International Journal of Advanced Manufacturing Technology, 40(3)(4), pp. 373-381 (2009).…”