Goodness of fit test using Lin-Wong divergence based on type-I censored data. (English) Zbl 07552810
Summary: Goodness of fit tests with two different methods are carried out in the present paper in order to recognize normal and exponential distributions within Type-I censored data. Here, we use the Lin-Wong divergence as our proposed measure of distance between distributions and compare its performance with that of other well known distance measures using an empirical distribution function and [C. E. Shannon, Bell Syst. Tech. J. 27, 379–423, 623–656 (1948; Zbl 1154.94303)], entropy concept. Furthermore, we present two real data analysis procedures using those proposed methods.
MSC:
| 62-XX | Statistics |
Keywords:
Anderson-Darling; Cramér-von Mises; exponentiality; kernel density; Kolmogorov-Smirnov; Kullback-Leibler; normalityCitations:
Zbl 1154.94303References:
| [1] | Abbasnejad, M.; Arghami, N. R.; Tavakoli, M., A goodness of fit test for exponentiality based on Lin Wong information, Journal of the Iranian Statistical Society, 11, 2, 191-202 (2012) · Zbl 1278.62058 |
| [2] | Alizadeh Noughabi, H., A new estimator of entropy and its application in testing normality, Journal of Statistical Computation and Simulation, 80, 10, 1151-62 (2010) · Zbl 1270.62021 |
| [3] | Bitaraf, M.; Rezaei, M.; Yousefzadeh, F., Test for normality based on two new estimators of entropy, Journal of Statistical Computation and Simulation, 87, 2, 280-94 (2017) · Zbl 07191938 |
| [4] | Cha, S. H., Comprehensive survey on distance/similarity measures between probability density functions, International Journal of Mathematical Models and Methods in Applied Sciences, 1, 4, 300-7 (2007) |
| [5] | Correa, J. C., A new estimator of entropy, Communications in Statistics-Theory and Methods, 24, 10, 2439-49 (1995) · Zbl 0875.62030 |
| [6] | Deza, M. M.; Deza, E., Encyclopedia of distance (2009), Heidelberg, Germany: Springer Berlin Heidelberg, Heidelberg, Germany · Zbl 1167.51001 |
| [7] | Ebrahimi, N.; Pflughoeft, K.; Soofi, E. S., Two measures of sample entropy, Statistics & Probability Letters, 20, 3, 225-34 (1994) · Zbl 0805.62009 |
| [8] | Esteban, M.; Castellanos, M.; Morales, D.; Vajda, I., Monte carlo comparison of four normality tests using different entropy estimates, Communication in Statistics-Simulation and Computation, 30, 4, 761-85 (2001) · Zbl 1008.62505 |
| [9] | Joarder, A.; Krishna, H.; Kundu, D., Inferences on weibull parameters with conventional Type-I censoring, Computational Statistics and Data Analysis, 55, 1, 1-11 (2011) · Zbl 1247.62061 |
| [10] | Koziol, J. A.; Byar, D. P., Percentage points of the asymptotic distributions of one and two sample KS statistics for truncated or censored data, Technometrics, 17, 4, 507-10 (1975) · Zbl 0326.62032 |
| [11] | Kullback, S.; Leibler, R. A., On information and sufficiency, The Annals of Mathematical Statistics, 22, 1, 79-86 (1951) · Zbl 0042.38403 |
| [12] | Lin, J.; Wong, S. K. M., A new directed divergence measure and its characterization, International Journal of General System, 17, 1, 73-81 (1990) · Zbl 0703.94003 |
| [13] | Lin, J., Divergence measures based on the shannon entropy, IEEE Transactions on Information Theory, 37, 1, 145-51 (1991) · Zbl 0712.94004 |
| [14] | Nelson, W., Applied life data analysis (1982), NewYork: JohnWiley and Sons, NewYork · Zbl 0579.62089 |
| [15] | Pakyari, R.; Balakrishnan, N., Testing exponentiality based on Type-I censored, Journal of Statistical Computation and Simulation, 83, 12, 2369-78 (2013) · Zbl 1453.62372 |
| [16] | Pakyari, R.; Nia, K. R., Testing goodness-of-fit for some lifetime distributions with conventional Type-I censoring, Communications in Statistics-Simulation and Computation, 46, 4, 2998-3009 (2017) · Zbl 1373.62501 |
| [17] | Park, S.; Shin, M., Kullback-leibler information of a censored variable and its applications, Statistics, 48, 4, 756-65 (2014) · Zbl 1326.62013 |
| [18] | Parzen, E., Nonparametric statistical data modeling, Journal of the American Statistical Association, 74, 365, 105-21 (1979) · Zbl 0407.62001 |
| [19] | Persson, T.; Rootzen, H., Simple and highly efficient estimators for a Type-I censored normal sample, Biometrika, 64, 1, 123-8 (1977) · Zbl 0352.62025 |
| [20] | Pettitt, A. N.; Stephens, M. A., Modified cramer-von mises statistics for censored data, Biometrika, 63, 2, 291-8 (1976) · Zbl 0329.62013 |
| [21] | Shannon, C. E., A mathematical theory of communication, ACM Sigmobile Mobile Computing and Communications Review, 5, 1, 3-55 (1948) |
| [22] | Shioya, H.; Da-Te, T., A generalization of lin divergence and the derivation of a new information divergence, Electronics and Communications in Japan (Part III: Fundamental Electronic Science), 78, 7, 34-40 (1995) |
| [23] | Silverman, B., Density estimation (1986), London, UK: Chapman & Hall/CRC, London, UK · Zbl 0617.62042 |
| [24] | Topsoa, F., Some inqualities for information divergence and related measures of discrimination, Research Report Collection, 2, 1, 73-83 (1999) |
| [25] | Vasicek, O., A test for normality based on sample entropy, Journal of Research Statistical Society, 38, Serial. B, 54-9 (1976) · Zbl 0331.62031 |
| [26] | Wasserman, L., All of nonparametric statistics (2010), New York: Springer Texts in Statistics, New York |
| [27] | Wieczorkowski, R.; Grzegorzewski, P., Entropy estimators - Improvements and comparisons, Communication Statistics Computing and Simulation, 28, 2, 541-67 (1999) · Zbl 0932.62007 |
| [28] | Zamanzade, E.; Arghami, N. R., Goodness of fit test based on correcting moments of modified entropy estimator, Journal of Statistical Computation and Simulation, 81, 12, 2077-93 (2011) · Zbl 1431.62026 |
| [29] | Zamanzade, E.; Arghami, N. R., Testing normality based on new entropy estimators, Journal of Statistical Computation and Simulation, 82, 11, 1701-13 (2012) · Zbl 1431.62202 |
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