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Full-Text Articles in Physical Sciences and Mathematics
Solutions Of The Problem Of Finding Confidence Intervals For The Two Normal Population With Unequal Variances, Ing-Haur Liu
Solutions Of The Problem Of Finding Confidence Intervals For The Two Normal Population With Unequal Variances, Ing-Haur Liu
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
Comparison of the means of two normal populations is a simpler problem when the variance (if unknown) are assumed to be equal than it is when they are not equal. The main concern of this report is the latter case also called the Behrens [4] - Fisher [5] problem.
In this report the solutions proposed by Behrens-Fisher, Scheffe [10], Welch [12], Banerjee [3] and Hajek [8], will be described and compared. To this problem Scheffe proposed a solution which has the advantage that no special table is necessary for its use, since the variate has an exact "Student's t" distribution. …
Nonparametric Test Of Fit, Frena Nawabi
Nonparametric Test Of Fit, Frena Nawabi
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
Most statistical methods require assumptions about the populations from which samples are taken. Usually these methods measure the parameters, such as variance, standard deviations, means, etc., of the respective populations. One example is the assumption that a given population can be approximated closely with a normal curve. Since these assumptions are not always valid, statisticians have developed several alternate techniques known as nonparametric tests. The models of such tests do not specify conditions about population parameters.
Certain assumptions, such as (1) observations are independent and (2) the variable being studied has underlying continuity, are associated with most nonparametric tests. However, …
Bayesian Estimate Of System Reliability, Naresh Shah
Bayesian Estimate Of System Reliability, Naresh Shah
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
A Bayesian estimate of reliability for each component in the system of n-components, each exponentially distributed, is developed which utilizes the basic notion of loss in estimation theory. Here we assume that each component is independently distributed. In reliability estimation, the loss associated with overestimation is usually greater than the loss associated with underestimation; and hence loss function can be a very useful tool. The prior distribution and loss function of reliability considered in this paper are flexible to be compatible with other situations in which reliability estimates are required. When the loss function is symmetric and no prior information …