Document Type : Final File

Author

Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran

Abstract

In this paper, we use two statistics for detecting outliers in exponentiated Pareto
distribution. These statistics are the extension of the statistics for detecting outliers in
exponential and gamma distributions. In fact, we compare the power of our test statistics
based on the simulation study and identify the better test statistic for detecting outliers in
exponentiated Pareto distribution. At the end, we describe an example from insurance
company.

Keywords

1. Adil I.H. and Irshad A.R. A Modified Approach for Detection of Outliers. Pak.j.stat.oper.res. 11 (1): 91-102 (2015).
2. Afify W.M. On estimation of the exponentiated Pareto distribution under different sample schemes. Stat. Methodol. 7 (2): 77-83 (2010).
3. Barnett V. and Lewis T. Outliers in Statistical Data. Second edn. John Wiley and Sons, New York (1984).
4. Dixit U.J. and Jabbari Nooghabi M. Efficient estimation in the Pareto distribution. Stat. Methodol. 7 (6): 687-691 (2010).
 
5. Gogoi B. and Das M.Kr. Detection of Multiple Upper Outliers in Exponential Sample under Slippage Alternative. IARJSET 2 (8): 63-69 (2015).
6. Hadi A.S., Imon A.H.M.R and Werner M. Detection of outliers. WIREs. Comp. Stat. 1 (1): 57–70 (2009).
7. Jabbari Nooghabi M., Jabbari Nooghabi H. and Nasiri P. Detecting Outliers in Gamma Distribution. Comm. Statist. Theory Methods 39 (4): 698–706 (2010).
8. Kale B.K. Detection of Outliers. Sankhya B 38: 356–363 (1976).
9. Kornacki A. Detection of outlying observations using the Akaike information criterion. Biometrical Letters 50 (2): 117-126 (2013).
10. Kumar N. Test for multiple upper outliers in an exponential sample irrespective of origin. Statistics 47 (1): 184-190 (2013).
11. Kumar N. and Lalitha S. Testing for upper outliers in Gamma sample. Comm. Statist. Theory Methods 41 (5): 820–828 (2012).
12. Lin Chien-tai and Balakrishnan N. Tests for Multiple Outliers in an Exponential Sample. Comm. Statist. Simulation Comput. 43 (4): 706-722 (2014).
13. Mahmoud M.A.E., Yhiea N.M. and El-Said S.M. Estimation of parameters for the exponentiated Pareto distribution based on progressively type-II right censored data. J. Egyptian Math. Soc. 24 (3): 431-436 (2016).
14. Nadarajah S. Exponentiated Pareto Distributions. Statistics 39 (3): 255-260 (2005).
15. Shawky A.I. and Abu-Zinadah H.H. Characterizations of the Exponentiated Pareto Distribution Based on Record Values. Applied Mathematical Sciences 2 (26): 1283-1290 (2008).
16. Shawky A.I. and Abu-Zinadah H.H. Exponentiated Pareto Distribution: Different Method of Estimations. Int. J. Contemp. Math. Sciences 4 (14): 677-693 (2009).
17. Zerbet A. and Nikulin M. A New Statistic for Detecting Outliers in Exponential Case. Comm. Statist. Theory Methods 32 (3): 573–583 (2003).