In this paper, two test statistics T k and Z k for testing multiple upper outliers in a Rayleigh ... more In this paper, two test statistics T k and Z k for testing multiple upper outliers in a Rayleigh sample are considered. The test statistic T k is a ratio of weighted sum of Y j s (Y j = X (j) − X (j−1) ; j = 2,. .. n) including upper outliers X (n−k+1) ,. .. , X (n) to all Y j 's and Z k is derived from the ratio of two maximum likelihood estimates. The critical values for Z k are obtained from the exact null distribution whereas the same for T k are approximated by a curve. Also the test T k is location and scale invariant. A simulation study is carried out to compare the performance of both tests with maximum likelihood ratio test.
Journal of Statistical Computation and Simulation, 2021
In this paper, we study the performance properties of the phase II exponential chart with an unkn... more In this paper, we study the performance properties of the phase II exponential chart with an unknown in-control (IC) rate parameter, used to monitor high-yield processes. The average time to signal (ATS) is used as the chart performance criterion instead of the usual average run length (ARL). Based on the IC conditional ATS (CATS) distribution, we examine the properties of both the equal-tailed and the ATS-unbiased exponential charts with estimated control limits and adjust the limits so that a nominal IC ATS performance is achieved. Two perspectives are investigated: the unconditional, under which the average of IC CATS distribution is set equal to a nominal ATS and, the conditional so that the IC CATS is set to or exceed a nominal ATS with a high probability. It is shown that the ATS-unbiased exponential chart under the conditional perspective has a better IC performance.
Communications in Statistics - Theory and Methods, 2015
The problem of multiple upper outliers in two-parameter exponential sample is considered. A test ... more The problem of multiple upper outliers in two-parameter exponential sample is considered. A test statistic is proposed to identify the outliers at the upper end of the sample. The null distribution of the test statistic is obtained and the critical values are found. The performance of the test is also compared with the earlier work.
Abstract An approach for testing multiple upper outliers with slippage alternative in an exponent... more Abstract An approach for testing multiple upper outliers with slippage alternative in an exponential sample, irrespective of origin, is discussed. The outlier detection procedure is based on a ratio of two estimates, obtained by the maximization of the two log-likelihood functions. One is the complete data log-likelihood and the other is its conditional expectation, given the regular observations. The exact null distribution of the test statistic is derived and no new table for critical values is required. A simulation study is also carried ...
Abstract In this paper, a test statistic for testing upper outliers with a slippage alternative, ... more Abstract In this paper, a test statistic for testing upper outliers with a slippage alternative, in an exponential sample is proposed. No tables for critical values are required as they can be calculated easily for any sample size. A simulation study is also carried out to compare the performance of the test with the maximum likelihood ratio test and other existing tests.
Procedure for detection of multiple outliers in a linear model is considered. The distribution of... more Procedure for detection of multiple outliers in a linear model is considered. The distribution of test statistic is derived under the null hypothesis. The Bonferroni inequality is used to obtain nominal upper percentage points. For a random sample from normal distribution, the proposed statistic reduces to the well known Murphy's test statistic. The performance of the test statistic is also studied and some simulation results are also presented.
In this paper, two test statistics T k and Z k for testing multiple upper outliers in a Rayleigh ... more In this paper, two test statistics T k and Z k for testing multiple upper outliers in a Rayleigh sample are considered. The test statistic T k is a ratio of weighted sum of Y j s (Y j = X (j) − X (j−1) ; j = 2,. .. n) including upper outliers X (n−k+1) ,. .. , X (n) to all Y j 's and Z k is derived from the ratio of two maximum likelihood estimates. The critical values for Z k are obtained from the exact null distribution whereas the same for T k are approximated by a curve. Also the test T k is location and scale invariant. A simulation study is carried out to compare the performance of both tests with maximum likelihood ratio test.
Journal of Statistical Computation and Simulation, 2021
In this paper, we study the performance properties of the phase II exponential chart with an unkn... more In this paper, we study the performance properties of the phase II exponential chart with an unknown in-control (IC) rate parameter, used to monitor high-yield processes. The average time to signal (ATS) is used as the chart performance criterion instead of the usual average run length (ARL). Based on the IC conditional ATS (CATS) distribution, we examine the properties of both the equal-tailed and the ATS-unbiased exponential charts with estimated control limits and adjust the limits so that a nominal IC ATS performance is achieved. Two perspectives are investigated: the unconditional, under which the average of IC CATS distribution is set equal to a nominal ATS and, the conditional so that the IC CATS is set to or exceed a nominal ATS with a high probability. It is shown that the ATS-unbiased exponential chart under the conditional perspective has a better IC performance.
Communications in Statistics - Theory and Methods, 2015
The problem of multiple upper outliers in two-parameter exponential sample is considered. A test ... more The problem of multiple upper outliers in two-parameter exponential sample is considered. A test statistic is proposed to identify the outliers at the upper end of the sample. The null distribution of the test statistic is obtained and the critical values are found. The performance of the test is also compared with the earlier work.
Abstract An approach for testing multiple upper outliers with slippage alternative in an exponent... more Abstract An approach for testing multiple upper outliers with slippage alternative in an exponential sample, irrespective of origin, is discussed. The outlier detection procedure is based on a ratio of two estimates, obtained by the maximization of the two log-likelihood functions. One is the complete data log-likelihood and the other is its conditional expectation, given the regular observations. The exact null distribution of the test statistic is derived and no new table for critical values is required. A simulation study is also carried ...
Abstract In this paper, a test statistic for testing upper outliers with a slippage alternative, ... more Abstract In this paper, a test statistic for testing upper outliers with a slippage alternative, in an exponential sample is proposed. No tables for critical values are required as they can be calculated easily for any sample size. A simulation study is also carried out to compare the performance of the test with the maximum likelihood ratio test and other existing tests.
Procedure for detection of multiple outliers in a linear model is considered. The distribution of... more Procedure for detection of multiple outliers in a linear model is considered. The distribution of test statistic is derived under the null hypothesis. The Bonferroni inequality is used to obtain nominal upper percentage points. For a random sample from normal distribution, the proposed statistic reduces to the well known Murphy's test statistic. The performance of the test statistic is also studied and some simulation results are also presented.
The industrial production process can be monitored from various perspectives. The objective of th... more The industrial production process can be monitored from various perspectives. The objective of the report is to perform quality control over some data and observe the whole process. The data 1 is taken from the paper titled "coal quality control with control charts". It's clear from the heading that the data associated with coal fresh from a mine which is to be used in industry purposes.
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Papers by Nirpeksh kumar