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is $\frac{Γ(r+x)}{Γ(r)Γ(x+1) }$ the same as ${r+x-1 \choose x}$?

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#statistics #negative-binomial
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E[1/(Y+1)] of negative binomial distribution

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#expected-value #binomial-distribution #negative-binomial
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Minimum Variance Estimators that Attain the Cramér-Rao lower bound

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#random-variables #maximum-likelihood #negative-binomial
274
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Uniformly minimum variance unbiased estimator for negative binomial distribution

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#statistics #statistical-inference #negative-binomial
32
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Hypothesis testing with the weighted average of negative binomial distributions

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#statistics #hypothesis-testing #negative-binomial
257
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Negative Binomial Series

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#probability #binomial-coefficients #binomial-theorem #negative-binomial
135
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Marginal Dirichlet Negative Binomial Distribution and the Multinomial Inverse Polya Urn

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#probability-distributions #stochastic-processes #negative-binomial #polya-urn-model
125
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Lower index of binomial coefficient becoming negative upon solving

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#binomial-coefficients #negative-binomial
74
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Negative binomial (and multinomial) extension to the minimum(failures,successes)

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#probability #negative-binomial #polya-urn-model #multinomial-distribution
155
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How to compare binomial distributions with different number of trial?

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#statistics #normal-distribution #binomial-distribution #negative-binomial
112
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How to evaluate $ \sum_{n=r}^{\infty} n^2 \binom{n-1}{r-1} p^r (1-p)^{n-r}$?

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#sequences-and-series #binomial-coefficients #closed-form #binomial-distribution #negative-binomial
44
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How was this simplification done?

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#power-series #binomial-coefficients #binomial-theorem #negative-binomial #euler-maclaurin
967
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An electronic scale in an automated filling operation stops the manufacturing line after five overweight packages are detected.

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#probability #expected-value #means #negative-binomial
46
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How to taylor expand $1/(1- \frac{k}{r})$ where k is some constant

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#taylor-expansion #binomial-theorem #negative-binomial #euler-maclaurin
179
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A negative binomial distribution for two random variables?

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#probability #negative-binomial

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