6, 1 INTRODUCTION
2. Fitting distributions
A well known mathematical distribution such as the normal distribut ion, transformations of the normal distribution or the incomplete gamma
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d i s t r i b u t i o n i s f i t t e d t o t h e p r i m a r y s e r i e s .
The m ethod h a s t h e a d v a n ta g e o f making t h e m o st ’ e f f i c i e n t ' u s e o f t h e a v a i l a b l e d a t a . E s t i m a t e s f o r a g iv e n r e t u r n p e r i o d a r e n o t
s t r o n g l y d e p e n d e n t on one o r two v a l u e s and a s a r e s u l t t h e r e i s g r e a t e r i n t e r v a l c o n s i s t e n c y . The method i s a l s o am enable t o e x t r a p o l a t i o n . However, b e c a u s e o f s a m p lin g e r r o r s , r e l a t i o n s h i p s b e tw e e n a n a l y s e s o f d i f f e r e n t d u r a t i o n s t e n d t o be i n c o n s i s t e n t , p a r t i c u l a r l y f o r t h e l a r g e r e t u r n p e r i o d s .
3. A t h i r d m ethod i s t o d e v e lo p r e l a t i o n s h i p s e i t h e r e m p i r i c a l l y o r by th e u s e o f d i s t r i b u t i o n f u n c t i o n s t o r e l a t e r a i n f a l l f o r any r e t u r n p e r i o d t o t h a t f o r two f i x e d r e t u r n p e r i o d s and f o r any d u r a t i o n t o two f i x e d d u r a t i o n s . The m ethod rem oves t h e p ro b lem o f i n t e r v a l i n c o n s i s t e n c i e s and c o n s i s t e n c y b e tw e e n n e i g h b o u r i n g s t a t i o n s i s r e l a t i v e l y e a s y t o o b t a i n . However t h e method can c r e a t e d i s c r e p a n c i e s b e tw e e n t h e e s i m a t e s p r o d u c e d
and p a s t r a i n f a l l e x p e r i e n c e . 4. The I n s t i t u t i o n o f E n g i n e e r s , A u s t r a l i a (1958) u s e d a f o r m u l a t o c a l c u l a t e r a i n f a l l i n t e n s i t y f o r a r e t u r n p e r i o d o f ' y ' y e a r s C y
(t^bp
(6.1) Py = r a i n f a l l i n t e n s i t y f o r a r e t u r n p e r i o d o f y y e a r s Fy i s t h e ' f r e q u e n c y f u n c t i o n ' and i s a f u n c t i o n o f t h e s t a n d a r d d e v i a t i o n o f t h e l o g a r i t h m s o f t h e p r i m a r y f a l l s and t h e r e t u r n p e r i o d t i s t h e d u r a t i o n o f t h e f a l l i n m i n u te s C, b and n a r e f u n c t i o n s o f g e o g r a p h i c l o c a t i o n .C h a r t s w ere p r o d u c e d from w hich e s t i m a t e s f o r any d u r a t i o n and any r e t u r n p e r i o d c o u l d be made f o r any p o i n t i n A u s t r a l i a .
The Institution of Engineers approach was greatly handicapped by very limited pluviograph data and an indirect approach was adopted to estimate rainfall for durations less than 24 hours and apart from the capital cities all estimates were based on the standard deviation of the calendar day primary rainfalls.
5. In connection with the analysis of Australian pluviograph data