ROBUST 2k FACTORIAL DESIGNS WITH LOGISTIC ERROR DISTRIBUTION
KrishiKosh
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Title |
ROBUST 2k FACTORIAL DESIGNS WITH LOGISTIC ERROR DISTRIBUTION
M.Sc. |
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Creator |
YADAV, SUNIL KUMAR
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Contributor |
Krishan Lal)
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Subject |
marketing, research methods, wood, paper, sampling, genetic processes, solutes, manpower, statistical methods, sets
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Description |
In designed experiment it is not always true that the error of the generated data follows the normal distribution which is one of the basic assumptions of analysis of variance. Under such situations, the maximum likelihood equations may not be linear and so are not solvable. The equations obtained from the first derivative of log likelihood function with respect to parameters do not yield the explicit solutions for the estimates due to nonlinearity of the function. Solving them by iterations is indeed problematic for reasons of (i) multiple roots, (ii) non-convergence of iterations, and (iii) convergence to wrong values. Therefore, methods have been developed using the modified maximum likelihood estimates in which the maximum likelihood equations are linearized by using the Taylor’s expansion and estimates of the parameters are obtained. These estimates are called modified maximum likelihood estimates. These estimates are efficient under non-normal error distribution and asymptotic to maximum likelihood estimates. In this dissertation, the error is assumed to follow logistic distribution and the model of factorial experiment is assumed to be fixed effect model and design considered is completely randomized design for equal number of observations per cell. Logistic distribution is negatively skewed, positively skewed or symmetric for the values of b1, b=1, respectively where b indicates the shape of generalized logistic distribution. We started with 23 factorial experiments and obtained the modified maximum likelihood estimates for all the effects (main effects and interaction effects) and the estimate of the error. F-statistics have been developed for all the treatment effects for testing the significance of parameters. These results have been generalized for the factorial experiments with k factors each at two levels. SAS code has been developed for the generation of data for 23 factorial experiments in which error follows logistic distribution for different values of parameter of logistic distribution. By using the SAS code, the generated data have been analysed and the compared the modified maximum likelihood procedure with the usual ANOVA procedure. Finally the size of the test is computed by using Monte Carlo simulation technique for different values of the parameter of the distribution. |
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Date |
2016-03-10T15:28:52Z
2016-03-10T15:28:52Z 2013 |
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Type |
Thesis
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Identifier |
http://krishikosh.egranth.ac.in/handle/1/65050
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Language |
en_US
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Format |
application/pdf
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Publisher |
IARI, IASRI, NEW DELHI
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