Let X1, ,Xn be a random sample from the inverse Gaussian distribution with pdf a Show that the statistics are sufficient and complete b For n 2, show that has an inverse Gaussian distribution, n Icirc raquo T has a X2n 1 distribution, and they are independent The inverse Gaussian distribution has many applications, particularly in modeling of lifetimes 2Tz3 71 X and Tm

Question: Let X1,... ,Xn be a random sample from the inverse Gaussian distribution with pdf a. Show that the statistics are sufficient and complete. b. For

Let X1,... ,Xn be a random sample from the inverse Gaussian with pdf

a. Show that the statistics

are sufficient and complete.
b. For n = 2, show that has an inverse Gaussian distribution, nÎ»/T has a X2n-1 distribution, and they are independent.
The inverse Gaussian distribution has many applications, particularly in modeling of lifetimes.

2Tz3 71 X and Tm

Step by Step Solution

★★★★★

3.45 Rating (177 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a This pdf can be written as This is an exponential f... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

941-M-S-P (8741).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Let X1, . . ., Xn be a random sample from an exponential population with parameter . Let Y1, . . ., Yn be the ordered random variables. (a) Show that the sampling distributions of Y1 and Yn are given...

Let X1, . . ., Xn be a random sample from a geometric distribution with pmf Show that pi = P (X = i) = pqi-l , i-1,2, ,0

Let X1, . . ., Xn be a random sample from the truncated exponential distribution with pdf Show that the MLE of y is min (Xi;). f(x) 0, otherwise

et X1, .... Xn be a random sample from the inverse Gaussian distribution with pdf For n = 1/2 F(x| A) = (24x)" exp (-2(x-4)7). 23 0

Random variables Let X1, ...,Xn be a random sample from the inverse Gaussian distribution with pdf A 1/2 -Me-)2 f(z| 4, A ) = e 0

Let X1, . . ., Xn be a random sample from exponential distribution with a mean of y. Show that Y1 = min (X1, X2, . . ., Xn) has an exponential distribution with mean y/n. Also, find the pdf of Yn =...

Let X1, . . . , Xn form a random sample from a distribution for which the p.d.f. or the p.f. is f (x|), where . Suppose that the value of must be estimated, and that T is a sufficient statistic...

Please answer clearly, thanks Let X1, ..., Xn be a random sample from the exponential distribution with x pdf: f (x) = =e B, x> 0. (a) Derive the distribution of Y = EL=1 Xi (b) Derive the MOME of B....

Please the answer the following question manually (This is the whole question, please don't comment "Missing graph, data or other material") Let X1, ..., Xn be a random sample from a N(0, o2)...

Mathematics 341/686 Assignment 2 Due Oct 26, 2015 in Class 1. Let X1 , . . . , Xn be a random sample from N (, 1). Assume a uniform (0, ) prior distribution for . (a) Find the posterior distribution...

Goliath Corporation issues $300,000 of bonds for $312,000. (a) Prepare the journal entry to record the issuance of the bonds, and (b) Show how the bonds would be reported on the balance sheet at the...

The door frames used in an industrialized building system are of one standard size. If the heights of adults are normally distributed, men with a mean of 1.73m and standard deviation of 0.064m and...

Q 6 : Of the sources of external funds for nonfinancial businesses in the United States, bonds account for approximately _ _ _ _ _ _ _ _ of the total Group of answer choices 8 0 % 3 0 % 5 0 % 5 %

Name some products that you believe have passed through the four stages of the international product life cycle. Try to identify industries or products for which the international product life cycle...

Draw a ball from an urn containing 6 black, 8 white, and 10 yellow balls. (a) Evaluate the probabilities of drawing a black (B), a white (W), or a yellow (Y) ball, separately. (b) Evaluate the...

Explain how Theorem 2.4: for events A and B: P(B) = P(A B)+P(A B) relates to the total probability formula: P(B) = P(A)P(B|A) + P(A)P(B|A).

Describe briefly, using your own words, the formalization of conditions [a] and [b] of a random experiment into a probability space (S, , P(.)).

What is the firm's optimal capital structure? (Calculate its corporate cost of capital at each structure. Also, note that data on component costs at alternative capital structures are not reliable in...

1. What amount comes closest to the present value of a 15-year annuity (a total of 15 consecutive payments) of $550 paid at the end of each year that does not begin until the end of the fourth year?...

The scores on a precision driving test for prospective drivers and transit company are normally distributed with a mean of 90 and a standard deviation of 15. a) What percentage of the tests have...