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

For ( ) , this implies that given 1 = 0 2 > 0 , if we take = � ( 0 0 + 1 ) ( 0 −1) 0 2 and = � ( 0 0 + 2 ) ( 0 −1) 0 2 , then �� ( 0 0 + 1 ) ( 0 −1) 0 2 � = −1 < 0 and �� ( 0 0 −1− 2 ) ( 0 −1) 0 2 � = 2 > 0 It follows that �� 0 0 + 1 ( 0 − 1) 0 2 � �� 0 0 − 1 − 2 ( 0 − 1) 0 2 � = − 2 < 0 This implies that there exists a sequence { } =1∞ ⊂ ( , ) and at least one point 0 ∈ ( , ) such that the sequence { } =1∞ converges to 0 ∈ ( , ) (i.e. ⟶ 0 ⟶ ∞ ) and ( 0 ) = 0 [1]. This completes the proof. ( , ) and ( , ) are intervals of normality corresponding to equation (6.8) and equation (6.9). This is the so-called interval of normality estimated by above mentioned authors using the Monte carol simulation method. Furthermore, it follows from equation (6.10), that we can define the functions and as such ( ) = − 2 0 + � 2 − 4 2 ( 0 − 1) (6.11) ( ) = − 2 2 ( 0 − 1) 0 + � 2 − 4 2 ( 0 − 1) (6.12) Also equation (6.11) and equation (6.12) are nonlinear problems of finding the zero(s) of and for every given value of , which can be solved using any of the iteration formula for finding the zero(s) (i.e. root) of a nonlinear equations [1]. In particular, in equation (6.10) , if we take = 1, 0 = −2, −1 2 ; as assumed by the authors in [10, 11] for a multiplicative time series model. We obtain the corresponding expressions for their respectively. R eferences R éférences R eferencias 1. R. Ferng. (1997). Lecture Notes on Numerical Analysis, National Chiao Tung University, Hsin-Chu, Taiwan, 1995. 2. George G. Roussas, (2007). A Course in Mathematical Statistics, Second Edition, Academic Press, USA, 1997. 3. U. A. Osisiogu, (1998). An Introduction to Real Analysis, Bestsort Educational Book. Nigeria, 1998. 4. M.R Spiegel, J.J Schiller and R. A. Srinivasan, (2000). Probability and Statistics, Second Edition, McGraw Hill Companies Inc., USA, 2000. 5. Iwueze Iheanyi S. (2007). Some Implications of Truncating the N (1, σ 2) Distribution to the left at Zero. Journal of Applied Sciences. 7(2) (2007) pp 189-195. 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. On the Generalized Power Transformation of Left Truncated Normal Distribution 1 Global Journal of Science Frontier Research Volume XXI Issue IV Year 2021 25 ( F ) © 2021 Global Journals Version I 1. R. Ferng. (1997). Lecture Notes on Numerical Analysis, National Chiao Tung University, Hsin-Chu, Taiwan, 1995. R ef