ON ESTIMATION FOLLOWING SELECTION FROM NONREGULAR DISTRIBUTIONS

Neeraj Misra; Edward C. van der Meulen

doi:10.1081/sta-100108447

ON ESTIMATION FOLLOWING SELECTION FROM NONREGULAR DISTRIBUTIONS

Communication in Statistics- Theory and Methods ◽

10.1081/sta-100108447 ◽

2001 ◽

Vol 30 (12) ◽

pp. 2543-2561 ◽

Cited By ~ 6

Author(s):

Neeraj Misra ◽

Edward C. van der Meulen

Keyword(s):

Nonregular Distributions

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Regular mles for nonregular distributions

Communication in Statistics- Theory and Methods ◽

10.1080/03610929908832404 ◽

1999 ◽

Vol 28 (9) ◽

pp. 2037-2044

Author(s):

Shaul K. Bar-Lev ◽

Camil Fuchs

Keyword(s):

Nonregular Distributions

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Solution of Euler’s Differential Equation in Terms of Distribution Theory and Fractional Calculus

Mathematics ◽

10.3390/math8122117 ◽

2020 ◽

Vol 8 (12) ◽

pp. 2117

Author(s):

Tohru Morita ◽

Ken-ichi Sato

Keyword(s):

Differential Equation ◽

Fractional Calculus ◽

Laplace Transform ◽

Nonstandard Analysis ◽

Distribution Theory ◽

Nonregular Distributions

For Euler’s differential equation of order n, a theorem is presented to give n solutions, by modifying a theorem given in a recent paper of the present authors in J. Adv. Math. Comput. Sci. 2018; 28(3): 1–15, and then the corresponding theorem in distribution theory is given. The latter theorem is compared with recent studies on Euler’s differential equation in distribution theory. A supplementary argument is provided on the solutions expressed by nonregular distributions, on the basis of nonstandard analysis and Laplace transform.

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