Estimation of the Parameters of the New Weibull-Pareto Distribution Using Ranked Set Sampling

Authors

  • Monjed H. Samuh Palestine Polytechnic University
  • Amer I. Al-Omari Al al-Bayt University
  • Nursel Koyuncu Hacettepe University

DOI:

https://doi.org/10.6092/issn.1973-2201/9368

Keywords:

New Weibull-Pareto distribution, Fisher information, Maximum likelihood estimation, Ranked set sampling

Abstract

The method of maximum likelihood estimation based on ranked set sampling (RSS) and some of its modifications is used to estimate the unknown parameters of the new Weibull-Pareto distribution. The estimators are compared with the conventional estimators based on simple random sampling (SRS). The biases, mean squared errors, and confidence intervals are used to the comparison. The effect of the set size and number of cycles of the RSS schemes are addressed. Monte Carlo simulation is carried out by using R. The results showed that the RSS estimators are more efficient than their competitors using SRS.

References

W. A. ABU-DAYYEH, S. A. AL-SUBH, H. A. MUTTLAK (2004). Logistic parameters estimation using simple random sampling and ranked set sampling data. Applied Mathematics and Computation, 150, no. 2, pp. 543–554.

A. D. AL-NASSER, A. I. AL-OMARI (2015). Information theoretic weighted mean based on truncated ranked set sampling. Journal of Statistical Theory and Practice, 9, no. 2, pp. 313–329.

A. I. AL-OMARI (2016). Quartile ranked set sampling for estimating the distribution function. Journal of the Egyptian Mathematical Society, 24, no. 2, pp. 303–308.

A. I. AL-OMARI, A. HAQ (2015). Entropy estimation and goodness-of-fit tests for the inverse Gaussian and Laplace distributions using paired ranked set sampling. Journal of Statistical Computation and Simulation, 86, no. 11, pp. 2262–2272.

M. F. AL-SALEH, Y. A. DIAB (2009). Estimation of the parameters of Downton's bivariate exponential distribution using ranked set sampling scheme. Journal of Statistical Planning and Inference, 139, no. 2, pp. 277–286.

M. F. AL-SALEH, M. H. SAMUH (2008). On multistage ranked set sampling for distribution and median estimation. Computational Statistics & Data Analysis, 52, no. 4, pp. 2066–2078.

M.A.ALJARRAH, F. FAMOYE, C. LEE (2015). A new Weibull-Pareto distribution. Communications in Statistics - Theory and Methods, 44, no. 19, pp. 4077–4095.

L. AMRO, M. H. SAMUH (2017). More powerful permutation test based on multistage ranked set sampling. Communications in Statistics - Simulation and Computation, 46, no. 7, pp. 5271–5284.

D. BASU (1956). The concept of asymptotic efficiency. Sankhya: The Indian Journal of Statistics, 17, no. 2, pp. 193–196.

D. S. BHOJ (1997). Estimation of parameters of the extreme value distribution using ranked set sampling. Communications in Statistics-Theory and Methods, 26, no. 3, pp. 653–667.

D. S. BHOJ, M. AHSANULLAH (1996). Estimation of parameters of the generalized geometric distribution using ranked set sampling. Biometrics, 52, no. 2, pp. 685–694.

M.CHACKO, P.Y.THOMAS (2008). Estimation of a parameter of Morgenstern type bivariate exponential distribution by ranked set sampling. Annals of the Institute of Statistical Mathematics, 60, no. 2, pp. 301–318.

V. CHOULAKIAN, M. STEPHENS (2001). Goodness-of-fit tests for the generalized Pareto distribution. Technometrics, 43, pp. 478–484.

A. C. DAVISON (2008). Statistical Models. Cambridge University Press, New York.

T. R. DELL, J. L. CLUTTER (1972). Ranked set sampling theory with order statistics background. Biometrics, pp. 545–555.

M. ESEMEN, S.GÜRLER (2017). Parameter estimation of generalized Rayleigh distribution based on ranked set sample. Journal of Statistical Computation and Simulation, 88, no. 4, pp. 615–628.

H. J.KHAMNEI, S.ABUSALEH (2017). Estimation of parameters in the generalized logistic distribution based on ranked set sampling. International Journal of Nonlinear Science,24, no. 3, pp. 154–160.

K. LAM, B. K. SINHA, Z. WU (1994). Estimation of parameters in a two-parameter exponential distribution using ranked set sample. Annals of the Institute of Statistical Mathematics, 46, no. 4, pp. 723–736.

G. A. MCINTYRE (1952). A method for unbiased selective sampling, using ranked sets. Australian Journal of Agricultural Research, 3, no. 4, pp. 385–390.

G. A. MCINTYRE (2005). A method for unbiased selective sampling, using ranked sets. The American Statistician, 59, pp. 230–232.

H. A. MUTTLAK (1997). Median ranked set sampling. Journal of Applied Statistical Science, 6, pp. 245–255.

S. NASIRU, A. LUGUTERAH (2015). The new Weibull-Pareto distribution. Pakistan Journal of Statistics and Operation Research, 11, no. 1, pp. 103–114.

J.NAVARRO, T. RYCHLIK, M. SHAKED (2007). Are the order statistics ordered? A survey of recent results. Communications in Statistics - Theory and Methods, 36, no. 7, pp. 1273–1290.

J. PAUL, P. Y. THOMAS (2017). Concomitant record ranked set sampling. Communications in Statistics - Theory and Methods, 46, no. 19, pp. 9518–9540.

R CORE TEAM (2018). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org.

H. M. SAMAWI, M. S. AHMED, W. ABU-DAYYEH (1996). Estimating the population mean using extreme ranked set sampling. Biometrical Journal, 38, no. 5, pp. 577–586.

M. H. SAMUH (2017). Ranked set two-sample permutation test. Statistica, 77, no. 3, pp. 237–249.

M. H. SAMUH, M. F.AL-SALEH (2011). The effectiveness of multistage ranked set sampling in stratifying the population. Communications in Statistics-Theory and Methods, 40, no. 6, pp. 1063–1080.

M. H. SAMUH, A. QTAIT (2015). Estimation for the parameters of the exponentiated exponential distribution using a median ranked set sampling. Journal of Modern Applied Statistical Methods, 14, no. 1, pp. 215–237.

S. SARIKAVANIJ, S. KASALA, B. K. SINHA, M. TIENSUWAN (2014). Estimation of location and scale parameters in two-parameter exponential distribution based on ranked set sample. Communications in Statistics-Simulation and Computation, 43, no. 1, pp. 132–141.

K. TAKAHASI, K. WAKIMOTO (1968). On unbiased estimates of the population mean based on the sample stratified by means of ordering. Annals of the Institute of Statistical Mathematics, 20, no. 1, pp. 1–31.

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Published

2020-06-25

How to Cite

Samuh, M. H., Al-Omari, A. I., & Koyuncu, N. (2020). Estimation of the Parameters of the New Weibull-Pareto Distribution Using Ranked Set Sampling. Statistica, 80(1), 103–123. https://doi.org/10.6092/issn.1973-2201/9368

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