Quantile Function for Rayleigh and Scaled Half Logistic: Application in Missing Data

Itrat Batool Naqvi; Muhammad Aslam

Itrat Batool Naqvi Department of Statistics, Forman Christian College University Lahore 54000, Pakistan
Muhammad Aslam Depatment of Statistics, King Abdulaziz University, Jeddah 21551, Saudi Arabia

Keywords: Control charts; Rayleigh, and scaled half logistic distribution; average run length.

Abstract

In this research paper quantile Functions for Scaled half logistic and Rayleigh distributions has been constructed. Data generated through the quantile Functions and then different limits for the full and missing data set have been developed with scale parameter. A number of such mean control limits could be constructed through purposed method but for analysis purpose few of them have discussed. The missing data limits broadened than the full data in each case, which was expected to be. The average run length (ARL) was also calculated for different sample sizes (50,100,150). The general decreasing behavior of ARL according to increasing shifts was observed that shows a worthy sign, for two distributions, as the probability of detecting an out of control signal increased due to decrease in ARL.

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