Abstract
In this paper, the derivation of the likelihood function for parameter estimation based on double ranked set sampling (DRSS) designs used by Sabry el.al.; (2019) for the estimation of the parameters of the power generalized Weibull distribution is considered. The developed likelihood function is then used for the estimation of the exponential Pareto distribution parameters. The maximum likelihood estimators (MLEs) are then investigated and compared to the corresponding ones based on simple random sampling (SRS) and ranked set sampling (RSS) designs. A Monte Carlo simulation is conducted and the absolute relative biases, mean square errors, and efficiencies are compared for the different designs. The relative efficiency of the DRSS estimates with respect to other designs was found to be higher in case of the exponential Pareto distribution (EP).
Highlights
McIntyre )1952(, proposed the ranked set sampling (RSS) design to help finding a more efficient estimate of the mean pasture yields
The extreme ranked set sampling (ERSS) design introduced by Samawi et al (1996), the median ranked set sampling (MRSS) design introduced by Muttlak (1997, 2003), the moving extreme ranked set sampling (MERSS) design introduced by Al-Odat and Al-Saleh (2001), modification in ratio estimator using rank set sampling introduced by Al-Odat (2009) and the multistage ranked set sampling (MSRSS) introduced by Al-Saleh and Al-Omari (2002)
It is clear that the model fitted under double ranked set sampling (DRSS) design is showing better results as compared to the other competitive models by providing smallest Akaike information criterion (AIC), corrected AIC (CAIC), Hannan-Quinn information criterion (HQIC) and Bayesian information criterion (BIC) which means that DRSS based models provide more accurate information about the true model used in this numerical example
Summary
McIntyre )1952(, proposed the RSS design to help finding a more efficient estimate of the mean pasture yields. According to Wolfe (2004), the procedure for obtaining the RSS samples can be summarized as follows: Step 1: Randomly select m2 units from a target population with cumulative distribution function (cdf) and probability. Step 3: Without yet knowing any values for the variable of interest, rank the units within each set with respect to variable of interest This may be based on personal professional judgment or done with concomitant variable correlated with the variable of interest. RSS uses only one observation, namely, X(11)k the lowest observation in the kth cycle, from this set, X(22)k the second lowest from another independent set of m observation, and X(mm)k the largest observation from a last set of m observations
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Pakistan Journal of Statistics and Operation Research
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
