Global Journal of Science Frontier Research, F: Mathematics and Decision Science, Volume 21 Issue 4

Remark 4.1 Further more observe that; 1) Iwueze (2007), for = 1, = 1 , the authors expressed [ ] in terms of cumulative distribution function of the standard normal distribution and [( − 1) 2 ] in terms of cumulative distribution function of the standard normal distribution and Chi- square distribution function, 2) Nwosu, Iwueze and Ohakwe (2010), for = 1, = −1, the authors expressed [ ] and [( − 1) 2 ] in terms of cumulative distribution function of the standard normal distribution and Gamma distribution function, 3) Ohakwe, Dike and Akpanta (2012), for = 1, = 2, the authors expressed [ ] and [( − 1) 2 ] in terms of cumulative distribution function of the standard normal distribution, 4) Nwosu, Iwueze, and Ohakwe. (2013), for = 1, = −1 , the authors expressed [ ] and [( − 1) 2 ] in terms of cumulative distribution function of the standard normal distribution and Chi-square distribution function, 5) Ibeh and Nwosu(2013), for = 1, = −2 , the authors expressed [ ] and [( − 1) 2 ] in terms of cumulative distribution function of the standard normal distribution and Chi-square distribution function, 6) Ajibade, Nwosu and Mbegdu (2015), for = 1, = −1 2 , the authors expressed [ ] and [( − 1) 2 ] in terms of cumulative distribution function of the standard normal distribution and Chi-square distribution function. Hence, it suffices to say that the expression for the moments is by no means unique. Furthermore, the aforementioned authors above seems to be somewhat restrictive in their estimation of moments; they all estimated only for the first moment about the origin (mean) and the second central moment (variance). Hence, in this paper such restriction is dispensed with. V. T he M oment G enerating F unction A ssociated with ( ; , , ) and ( ; , ) The moment generating function of is given by ( ; , , ) = ( ; , , ) = � ( ; , , ) ∞ 0 = � � ( ) ! . ≥0 ( ; , , ) ∞ 0 Observe that the series ∑ ( ) ! ∞=0 converges uniformly (by ratio test) [3,13], hence by Taylors series expansion, for some positive constant (sufficiently large enough), there exists a number ( ) between 0 and such that ( ) ⟶ 0 as ⟶ ∞ [3,13], it then follows that as ⟶ ∞ � �� 1 ! ( ) + 1 ! ( )( ( )) � =0 ( ; , , ) ∞ 0 can be approximated by On the Generalized Power Transformation of Left Truncated Normal Distribution 1 Global Journal of Science Frontier Research Volume XXI Issue IV Year 2021 19 ( F ) © 2021 Global Journals Version I 3. U. A. Osisiogu, (1998). An Introduction to Real Analysis, Bestsort Educational Book. Nigeria, 1998. R ef