Goodness of t tests for logistic distribution based on Phi-divergence


Abstract


Some goodness of fit tests for logistic distribution based on Phi-divergenceare developed. The powers of the introduced tests are compared with sometraditional goodness of t tests including Kolmogorov-Smirnov, Anderson-Darling and Cramer-von Mises tests for logistic distribution using MonteCarlo simulation. It is shown the proposed tests have good performance ascompared with their competitors in the literature. A real data set is used forillustration.

DOI Code: 10.1285/i20705948v11n1p185

Keywords: Logistic distribution; Phi-divergence; Goodness of t tests; Kolmogorov-Smirnov; Anderson-Darling.

References


Alizadeh Noughabi, H. and N. Balakrishnan (2016). Tests of goodness of t based on Phi-divergence. Journal of Applied Statistics, 43 (3): 412-429.

Alizadeh Noughabi, H. and Park, S. (2016). Tests of t for the Laplace distribution based on correcting moments of entropy estimators. Journal of Statistical Computation and Simulation, 86 (11): 2165-2181.

Alizadeh Noughabi, H. and Arghami, N.R. (2013). General treatment of goodness-of-t tests based on Kullback{Leibler information. Journal of Statistical Computation and

Simulation, 83 (18): 1556-1569.

Al-Omari, A.I. and Haq, A. (2016). Entropy estimation and goodness-of-t tests for the inverse Gaussian and Laplace distributions using paired ranked set sampling. Journal

of Statistical Computation and Simulation, 86 (11): 2262-2272.

Anderson, T. W., & Darling, D. A. (1954). A test of goodness of t. Journal of the American Statistical Association, 49 (268), 765-769.

Bain L.J. and Englehardt, M. (1973). Interval estimation for the two parameter double exponential distribution. Technometrics, 15, pp. 875{887.

Csiszar, I. (1963). Eine information's theoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizitat von Markoschen Ketten, Magyar Tud. Akad. Mat.

Kutato Int. Kozl, 8: 85{108.

Csiszar, I. (1967). On topology properties of f-divergences. Studia Scientiarum Mathematicarum Hungarica, 2: 329{339.

Kolmogorov, A.N. (1933). Sulla Determinazione Empirica di une legge di Distribuzione,

Giornale dell'Intituto Italiano degli Attuari, 4; 83{91.

Puig, P. and Stephens, M.A. (2000). Tests of t for the Laplace distribution with

applications. Technometrics, 42(4)

Silverman, B.W. (1986). Density Estimation for Statistics and Data Analysis, Chap-

man and Hall, London.

Vajda, I. (1989). Theory of Statistical Inference and Information, Kluwer Academic Publishers, Bostont Von Mises, R. (1932). Wahrscheinlichkeitsrechnung und ihre Anwendung in der

Statistik und theoretischen Physik. Bulletin of the American Mathematical Society, 38: 169-170.

Zamanzade, E. and Arghami, N.R. (2011). Goodness-of-t test based on correcting moments of modied entropy estimator. Journal of Statistical Computation and Simulation, 81 (12) 2077-2093.

Zamanzade, E. and Mahdizadeh. M (2017). Goodness-of-t tests for Rayleigh distribution based on Phi-divergence. Revista Colombiana de Estadstica, 40 (2), 279-290.

Zhang, C. and Cheng, B. (2003). Binning methodology for nonparametric goodness-of-t test. Journal of Statistical Computation and Simulation, 73(1): 71{82.


Full Text: pdf
کاغذ a4
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.