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

can be approximated by −1 2 2 � n − 2 2 2 � 1 ! � 2 � =0 du ∞ 0 = −1 2 2 � 1 2 ! =0 � r+n − 2 2 2 ∞ 0 Let = 2 2 2 ; ⟹ 2 = , then substituting appropriately into the integral above and simplifying, we have −1 2 2 � 1 2 ! =0 2 � r+n −1 (2 ) r+n −1 2 − ∞ 0 = −1 2 2 � 2 r+np−1 2 r−n −1 ! =0 � � r+n +1 2 �−1 − ∞ 0 = −1 2 2 ∑ 2 r+np+1 2 r ! =n Γ � r + + 1 2 � 2 n +2 √2 Φ � − � Thus, [ ; , , ] = −1 2 2 ∑ 2 r+np +1 2 r ! =⌊− ⌋ Γ� r+ +1 2 � 2 np +1 √2 Φ� − � (4.2) And ( , , ) = �( − ) ; , , � = �(−1) − � − � − −1 =0 [ ; , , ] + � ; , , � = �(−1) − � − � − −1 =0 −1 2 2 ∑ 2 r+np+1 2 r ! =⌊− ⌋ Γ � r + + 1 2 � 2 n +2 √2 Φ � − � + −1 2 2 ∑ 2 r+jn +1 2 r ! =⌊− ⌋ Γ � r + j + 1 2 � 2 +2 √2 Φ � − � = ∑ (−1) − � − � − =0 −1 2 2 ∑ 2 r+np +1 2 r ! =⌊− ⌋ Γ� r+ +1 2 � 2 n +2 √2 Φ� − � (4.3) Where ⌊ ⌋ is the greatest integer function less than . It is important to observe that in particular, in equation (4.2) , if we take = −1 , then is an inverse transform of and by putting = 7, = 1 and evaluating [ ; 1, , −1] at = 1, 2 respectively, we obtain the result in [6]. On the Generalized Power Transformation of Left Truncated Normal Distribution © 2021 Global Journals 1 Global Journal of Science Frontier Research Volume XXI Issue IV Year 2021 18 ( F ) Version I 6. Nwosu C. R, Iwueze I.S. and Ohakwe J. (2010). Distribution of the Error Term of the Multiplicative Time Series Model Under Inverse Transformation. Advances and Applications in Mathematical Sciences. Volume 7, Issue 2, 2010, pp. 119 – 139. R ef