Whipple Distibution For Estimating The Approximate Reliability Function Of Intentional Downtime For Mammogram Device (contaminated data)

Abstract

In this research, the abnormality of some observations, their deviation or their distance from the largest part of the observations that are present with them in the majority of natural phenomena, is called those deviant quarrels called "outliers" or contaminations, which, if they are within the data, the traditional capabilities and because of Penetration of the basic conditions of it fails to give accurate estimates of the parameters of the statistical community from which that data was withdrawn so the use of traditional capabilities for data containing contaminated values is a real problem due to the inefficiency of these capabilities, therefore investigation and search for methods to purify these data should be investigated. Anomalies (pollutants) first, then conducting the estimate for the purpose of reaching efficient estimates for the estimated parameters and then to an efficient estimate of the reliability function. In this paper, the approximate reliability of the ferrite distribution is estimated if the data contains k contaminated values (anomalies) that arise from the deviation of the original values of the data using the anomaly of the Dixit, which will be used to find the common distribution of data in the event that it contains an anomaly, so the ferrite distribution was used As the original distribution of data,the basic data was contaminated with k from the values. The distribution follows the Whipple distribution as a case, and the Freit distribution parameters were estimated using the maximum possible method and the placement method and the linear placement method to estimate the distribution parameters in both cases, and then compensated for the estimates of those methods in a function with The mechanism of the Freit distribution to obtain the approximate reliability of the distribution, and then compare the estimation methods using the criteria of the average integral error squares IMSE and reached the best way to estimate the approximate reliability function in the presence of contaminated data is the greatest possible method with a priority rate of 34% when the contaminated distribution is wet. Followed by the placement method with a preference rate of 16% when the polluted distribution is Weibel, then the linear placement method with a priority rate of 0% for both polluted distributions. The estimated reliability by the greatest possible method R ̂_Mle approaches more than the real reliability of the placement method R ̂_Mom and the linear placement method R ̂_LMom, At recorded plucks the method of preference for the rest of the methods for some simulation experiments. And the greatest possible method is more suitable for real data, which represents the failure times for the mammogram, which is used to detect breast cancer