Approximate Confidence Intervals For An Exponential Parameter From A Sequential Life Test PDF Download
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| Author | : Kenneth Brian Fairbanks |
| Publisher | : |
| Total Pages | : 37 |
| Release | : 1979 |
| Genre | : Estimation theory |
| ISBN | : |
Download Approximate Confidence Intervals for an Exponential Parameter from a Sequential Life Test Book in PDF, ePub and Kindle
A sequential life test for the exponential location parameter was given by Epstein and Sobel (1955). This sequential test may be modified by truncating the test at r sub 0 failures and/or at total test time t'. There may be a need or a desire to also estimate the parameter after the test decision, using the test data. Bryant and Schmee (1979) have given confidence intervals for the mean lifetime, theta, from a truncated sequential test scheme, using methods which depend heavily on numerical techniques using a computer. A more flexible approach is considered using a martingale inequality which was also given by Wald (1947) in another context. Interval estimates are found which are functions of a positive constant d which must be chosen less than an upper bound which is itself a function of the number of failures observed. It is suggested that d be chosen as a function of the sample path (i.e., after the test is complete). The validity of the confidence coefficient comes into question if this posterior selection of d is employed. Simulation studies indicate that the resulting intervals are usually conservative.
| Author | : STANFORD UNIV CALIF DEPT OF STATISTICS. |
| Publisher | : |
| Total Pages | : 23 |
| Release | : 1977 |
| Genre | : |
| ISBN | : |
Download Confidence Intervals Related to Sequential Tests for the Exponential Distribution Book in PDF, ePub and Kindle
One sided sequential tests for the mean of an exponential distribution are proposed, and the related confidence intervals are computed. The tests behave like the classical sequential probability ratio test when the mean is small and like a fixed time test when the mean is large and accurate estimation is important. (Author).
| Author | : Kenneth Brian Fairbanks |
| Publisher | : |
| Total Pages | : 66 |
| Release | : 1978 |
| Genre | : Estimation theory |
| ISBN | : |
Download Two Sided Confidence Intervals for an Exponential Parameter from a Life Test with Type I and Type II Censoring Book in PDF, ePub and Kindle
A life test on items assumed to have an exponential lifetime is often designed with type I censoring, type II censoring or both. In type I censoring, n items are placed on test and observed for a fixed time t*, while in type II censoring the test terminates with the rth failure, where r is a preassigned integer. If these schemes are combined, the test terminates at min(t*, tau sub r) where Tau sub r is the time of the rth failure. Procedures for estimating the exponential parameter from this combined scheme were first considered by Epstein. Epstein established one sided confidence intervals for this parameter. This report reviews Epstein's work and establishes two sided confidence intervals. The confidence intervals are expressed in terms of time on test and chi-square percentiles with the degrees of freedom depending on the number of observed failures. An expression for the expected length of the confidence intervals is also derived. (Author).
| Author | : |
| Publisher | : |
| Total Pages | : 1048 |
| Release | : |
| Genre | : Science |
| ISBN | : |
Download Technical Abstract Bulletin Book in PDF, ePub and Kindle
| Author | : |
| Publisher | : |
| Total Pages | : 992 |
| Release | : 1986 |
| Genre | : Aeronautics |
| ISBN | : |
Download Scientific and Technical Aerospace Reports Book in PDF, ePub and Kindle
| Author | : Jan Cornelius Geertsema |
| Publisher | : |
| Total Pages | : 158 |
| Release | : 1968 |
| Genre | : Probabilities |
| ISBN | : |
Download Sequential Confidence Intervals Based on Rank Tests Book in PDF, ePub and Kindle
| Author | : William Eugene Coleman |
| Publisher | : |
| Total Pages | : 27 |
| Release | : 1970 |
| Genre | : Mathematics |
| ISBN | : |
Download A Comparison of Confidence Interval Procedures in Censored Life Testing Problems Book in PDF, ePub and Kindle
Obtaining a confidence interval for a parameter lambda of an exponential distribution is a frequent occurrence in life testing problems. Oftentimes the test plan used is one in which all the observations are censored at the same time point. Several approximate confidence interval procedures are available in the statistical literature; however, to the knowledge of the author, the performance characteristics of the various approximations used in these procedures have not been established analytically. The purpose of this paper is to report the results of an empirical study of the performance of four of these procedures with respect to the expected length of the interval, the variance of the interval length, and the coverage probability. (Author).
| Author | : |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 1970 |
| Genre | : |
| ISBN | : |
Download A Comparison of Confidence Interval Procedures in Censored Life Testing Problems Book in PDF, ePub and Kindle
Obtaining a confidence interval for a parameter lambda of an exponential distribution is a frequent occurrence in life testing problems. Oftentimes the test plan used is one in which all the observations are censored at the same time point. Several approximate confidence interval procedures are available in the statistical literature; however, to the knowledge of the author, the performance characteristics of the various approximations used in these procedures have not been established analytically. The purpose of this paper is to report the results of an empirical study of the performance of four of these procedures with respect to the expected length of the interval, the variance of the interval length, and the coverage probability. (Author).
| Author | : Kenneth Brian Fairbanks |
| Publisher | : |
| Total Pages | : 34 |
| Release | : 1979 |
| Genre | : Estimation theory |
| ISBN | : |
Download Confidence Intervals for an Exponential Parameter from a Two Stage Life Test Book in PDF, ePub and Kindle
The two stage life test of Bulgren and Hewett (1973) for the mean lifetime, theta, of an exponentially distributed lifetime is essentially a two stage version of type 2 censoring. Since the test decision only determines whether theta is above or below theta sub 0, it may be of interest to estimate theta following the decision using the test data. Epstein (1960a) found confidence intervals for under type 2 censoring. This report shows that Epstein's intervals may be modified slightly and used to provide confidence intervals for theta following the two stage test. The resulting confidence intervals are shown to be conservative. (Author).
| Author | : Sheldon M. Ross |
| Publisher | : Academic Press |
| Total Pages | : 706 |
| Release | : 2020-09-11 |
| Genre | : Mathematics |
| ISBN | : 0128177470 |
Download Introduction to Probability and Statistics for Engineers and Scientists Book in PDF, ePub and Kindle
Introduction to Probability and Statistics for Engineers and Scientists, Sixth Edition, uniquely emphasizes how probability informs statistical problems, thus helping readers develop an intuitive understanding of the statistical procedures commonly used by practicing engineers and scientists. Utilizing real data from actual studies across life science, engineering, computing and business, this useful introduction supports reader comprehension through a wide variety of exercises and examples. End-of-chapter reviews of materials highlight key ideas, also discussing the risks associated with the practical application of each material. In the new edition, coverage includes information on Big Data and the use of R. This book is intended for upper level undergraduate and graduate students taking a probability and statistics course in engineering programs as well as those across the biological, physical and computer science departments. It is also appropriate for scientists, engineers and other professionals seeking a reference of foundational content and application to these fields. Provides the author’s uniquely accessible and engaging approach as tailored for the needs of Engineers and Scientists Features examples that use significant real data from actual studies across life science, engineering, computing and business Includes new coverage to support the use of R Offers new chapters on big data techniques
