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

( ) = �( − ) 1 −1 | | √2 Φ � − � −1 2 � 1 − � 2 ∞ 0 = � �(−1) − � − � − =0 1 −1 | | √2 Φ � − � −1 2 � 1 − � 2 ∞ 0 = �(−1) − � − � − =0 � + 1 −1 | | √2 Φ � − � −1 2 � 1 − � 2 ∞ 0 = ∑ (−1) − � − � − =0 [ ; , , ] (4.1) and we proceed to compute the ℎ moment about the origin [ ; , , ] which is given by [ ; , , ] = � 1 −1 | | √2 Φ � − � −1 2 � 1 − � 2 ∞ 0 = � + 1 −1 −1 2 � 1 − � 2 ∞ 0 Let = 1 ; ⟹ = 1− 1 du , substituting into the integral above and simplifying, we have � + 1 −1 −1 2 � 1 − � 2 1− 1 du ∞ 0 = � n −1 2 � 2 −2 +1� du ∞ 0 = −1 2 2 � n − 2 2 2 2 du ∞ 0 = −1 2 � n − 2 2 2 � � 2 � ! . ≥0 du ∞ 0 Observe that the series ∑ � 2 � ! . ≥0 converges uniformly (by ratio test) [3,13], hence by Taylors series expansion, for some positive constant (sufficiently large enough) [3,13], there exists a number ( ) between 0 and 2 such that ( ) ⟶ 0 as ⟶ ∞ , it then follows that as ⟶ ∞ −1 2 2 � n − 2 2 2 �� 1 ! � 2 � + 1 ! � 2 � � ( )� � =0 du ∞ 0 On the Generalized Power Transformation of Left Truncated Normal Distribution 1 Global Journal of Science Frontier Research Volume XXI Issue IV Year 2021 17 ( F ) © 2021 Global Journals Version I 3. U. A. Osisiogu, (1998). An Introduction to Real Analysis, Bestsort Educational Book. Nigeria, 1998. R ef