For known k, show that the negative binomial distribution (4.12) has exponential family form (4.1) with natural

Question:

For known k, show that the negative binomial distribution (4.12) has exponential family form (4.1) with natural parameter log[µ/(µ + k)].

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Categorical Data Analysis

ISBN: 9780471360933

2nd Edition

Authors: Alan Agresti

See More Books

Question Posted: Dec 16, 2022 05:56 AM

See More Questions

The negative binomial distribution with parameters r and p, where r is known and p is unknown (0 < p < 1);
Show that the negative of z = r (cos + i sin ) is - z = r [cos ( + ) + i sin ( + )].
The negative binomial distribution is sometimes defined in a different way as the distribution of the number of failures that precede the kth success. If the kth success occurs on the xth trial, it...
WSU Small Business Booster Every year, Robin identifies a small business to invest her money in because she wants to support companies that WSU students have started. Robin named the program WSU...
What is the difference between small businesses and high-growth ventures?
Assume that Penguin Co. is considering disposing of equipment that cost $50,000 and has $40,000 of accumulated depreciation to date. Penguin Co. can sell the equipment through a broker for $25,000...
Zinc has a work function of $4.3 \mathrm{eV}$. a. What is the longest wavelength of light that will release an electron from a zinc surface? b. A $4.7 \mathrm{eV}$ photon strikes the surface and...
Proctor & Gamble is a well-known consumer products company that owns a variety of popular brands. A recent news article contained the following information: CINCINNATI, March 9...
Question 2-1: Consider the conductor in the diagram above, with an excess charge Q. As just argued above, there is zero electric field within the conductor. What is the amount of excess charge...
Joy's Frozen Yogurt shops have enjoyed rapid growth in northeastern states in recent years. From the analysis of joy's various outlets, it was found that die demand curve follows this pattern: Q =...
Show that the sample value of the uncertainty coefficient (2.13) satisfies U = G 2 / 2n(p +j ). [Haberman (1982) gave its standard error.]
Show representation (4.18) for the binomial distribution.
Find the following. (a) (b) (c) (d) (e) (f) || n ||
In the US, the proportion of adults who are allerge to peanuts is 0.01. Suppose that ten individuals were selected independently of each other. Let x equals the number of people with a peanut...
The Jamaican labour laws/regulations are irrelevant in today's society given that organizations have been developing sound industrial relations policies and programmes to maintain sound, harmonious...
The school tennis league consists of 12 players. Daniel has a 30% chance of winning any game against a higher-ranked player, and a 70% chance of winning any game against a lower-ranked player. If...
Write a 1400 word essay (MLA format) on the topic following: How Canadian Labour law have changed through history? Include the following. 1. What is Labour law? How much has it changed and developed?...
You have recently been hired as the HR manager for KM Contracting, a medium-sized construction company with offices throughout Canada. Many of the company's trades employees are unionized, and one of...
Suppose f C[a, b] and f'(x) exists on (a, b). Show that if f'(x) 0 for all x in (a, b), then there can exist at most one number p in [a, b] with f (p) = 0.
It is possible to investigate the thermo chemical properties of hydrocarbons with molecular modeling methods. (a) Use electronic structure software to predict cHo values for the alkanes methane...
Consider Example 13 about the power of the test of H 0 : p = 0.1 against H a : p > 0.1 used to test the effectiveness of a manual therapy in opening blocked tubes, where p is the probability of at...
For testing H 0 : p = 1/3 (astrologers randomly guessing) against H a : p > 1/3 with n = 116, Example 12 showed that P(Type II error) = 0.02 when p = 0.50. Now suppose that p = 0.35. Recall that...
A marketing study conducts 60 significance tests about means and proportions for several groups. Of them, 3 tests are statistically significant at the 0.05 level. The studys final report stresses...
Consider a bond with a 10% coupon rate and a yield to maturity of 8%. What kind of bond is it? (Par, discount, premium). If the bonds yield to maturity remains constant, in one year will the bond...
Using the input data below, how do I calculate the breakeven point for each of the following in excel: Procedures per day, Net revenue per procedure, supply cost? INPUT DATA: KEY OUTPUT: Land initial...
You are able to purchase a mortgage note from a bank for $429,000 that gives you the right to receive $75,500 in each of the next 7 years. What is the yield on this investment? Mr. Able owns a...

For known k, show that the negative binomial distribution (4.12) has exponential family form (4.1) with natural

Question:

Step by Step Answer:

The negative binomial distribution is defined as the probability mass functi...View the full answer

Categorical Data Analysis

Students also viewed these Mathematics questions