Exponential distribution - poisson distribution function, Civil Engineering

Exponential distribution - Poisson distribution function:

Let X follow exponential distribution with parameter θ. Find the pdf of

Y = X1/β where  β( ≥ 1 ) is a constant.

Solution :

The function Y = X1/β is one to one in the interval ( 0,∞) where pdf of X is non zero. The inverse of the transformation Y = X1/β is X - Yβ which gives dX/dY =β Yβ-1. Also

fx(x) = 1/θ e-x/θ , x> 0.

Hence

f(y) = f(g-1(y))¦ dg-1(y)/dy ¦

=1/θ e -yβ/θ ¦β yβ-1¦, y>0

and the pdf is

f(y) = β y β -1/θ e -yP/θ , y>0 with parameters θ >0,β ≥ 1

Remark:

The distribution of Y, just derived Example 4, is known as Weibull distribution. That has application is life testing. Remember that if Y follows Weibull distribution with parameters θ and β then Yβ follows the exponential distribution with parameter θ.

The treatment of distribution of functions of more than one variable is similar. However, care should be taken to determine the correct region of variation of the variables under the transformation and use it properly for obtaining the marginal distributions. We assume an example to illustrate the point.

Posted Date: 1/30/2013 7:08:55 AM | Location : United States







Related Discussions:- Exponential distribution - poisson distribution function, Assignment Help, Ask Question on Exponential distribution - poisson distribution function, Get Answer, Expert's Help, Exponential distribution - poisson distribution function Discussions

Write discussion on Exponential distribution - poisson distribution function
Your posts are moderated
Related Questions
describe the two fundermental purposes of surveying

who invented the first LA abrasion test machine

Define Recommendations for confined elastomeric pad?  (a) Permissible limits for confined pressure on elastomer pad depends upon effectiveness of internal seal preventing it fr

A circular footing is resting on a stiff saturated clay with qu = 250 kN/m 2 . The depth of foundation is 2 m. Verify the diameter of the footing if the column load is 600 kN. S

Types of Surveys and Investigations: For preparing a good road project, the following surveys and investigations are needed: (a)        Traffic Surveys (b)       Topogr

Question Can all utility detectors detect depth of utilities ? Answer In Hong Kong, underground utility detectors are as a rule separated into two categories- electro

Solve the following problems related to Wastewater flow and densities (a) The volume of 896, 000 lb of wastewater is? (b)  The weight of 13,000 ft3 of wastewater is? (c) A

Define Unit Hydrograph UNIT HYDROGRAPH: The hydrograph developed for a drainage basin (watershed) from the runoff of a 1 in or 1 cm storm. It is the base hydrograph from which

why strength of transition zone is less than bulk paste

difination of magnative bearing