The exact distribution of the maximum likelihood estimators for the linear regression negative exponential model |
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| Affiliation: | 1. Department of Economics, University of Western Ontario, London, Cont., Canada N6A 5C2;2. Birkbeck College, London University UK;1. Interdisciplinary Graduate School of Engineering Science, Kyushu University, 6-1 Kasugakoen, Kasuga, Fukuoka, Japan;2. Institute for Materials Chemistry and Engineering Kyushu University, 6-1 Kasugakoen, Kasuga, Fukuoka, Japan;1. Department of Mechanical Engineering, Institute of Technology and Management, Gida, Gorakhpur 273209, India;2. Department of Mechanical Engineering, Bundelkhand Institute of Engineering and Technology, Jhansi 284128, India;1. Faculty of Engineering & Computing, Coventry University, Coventry CV12JH, UK;2. Mechanical Engineering Department, Frederick University, Nicosia 1093, Cyprus |
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| Abstract: | The exact distribution of the maximum likelihood estimators in an exponential regression model are derived. The approach involves finding the distribution of the score statistic, since the log likelihood is globally concave, and then using the one-to-one correspondence between this and the estimator. The distribution is a weighted sum of independent exponential random variables. The exact p.d.f. is found by inverting the characteristic function by a straightforward application of residue theory. |
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