Question

For a random sample from the distribution $f(x)=e^{-(x-\theta)} , x>\theta$ , show that $2n[X_{(1)}-\theta]\sim\chi^2_{2}$

score 1.9k · Answer 1 · 2026-04-16 00:45:06

1.9k

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For a random sample from the distribution $f(x)=e^{-(x-\theta)} , x>\theta$ , show that $2n[X_{(1)}-\theta]\sim\chi^2_{2}$

Published on 16 Apr 2026 - 0:45

score 39 · Answer 2 · 2026-04-15 11:23:13

39

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Probabilities in Matching to the closest point

Published on 15 Apr 2026 - 11:23

score 41 · Answer 3 · 2026-03-25 11:06:42

41

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What is the probability that the inequality $Y_{(m')}<X_{(m+1)}<Y_{(m'+1)}$ will hold?

Published on 25 Mar 2026 - 11:06

score 113 · Answer 4 · 2026-04-15 04:03:01

113

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Showing that $\frac{X_{(i)}}{X_{(n)}},i=1,2,...,n-1$ and $X_{(n)}$ are independent for a population with df $F(y)=y^{\theta}$

Published on 15 Apr 2026 - 4:03

score 89 · Answer 5 · 2026-04-17 10:30:13

89

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Show that $Y_1=\frac{X_{(1)}}{X_{(2)}},Y_2=\frac{X_{(2)}}{X_{(3)}},\dots, Y_{n-1}=\frac{X_{(n-1)}}{X_{(n)}}$, and $Y_{(n)}=X_{(n)}$ are independent

Published on 17 Apr 2026 - 10:30

score 385 · Answer 6 · 2026-04-15 03:37:41

385

Views

Distribution of a sample IQR

Published on 15 Apr 2026 - 3:37

score 65 · Answer 7 · 2026-04-16 05:26:11

65

Views

A random vector of continuous random variables and its Order Statistics

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score 277 · Answer 8 · 2026-04-12 07:07:16

277

Views

Finding complete sufficient statistic

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score 873 · Answer 9 · 2026-05-10 12:51:50

873

Views

Expected maximum pairwise distance for $n$ points on a circle?

Published on 10 May 2026 - 12:51

score 36 · Answer 10 · 2026-04-14 17:28:50

36

Views

Is there an explicit expression for the density of a data point minus the sample median?

Published on 14 Apr 2026 - 17:28

score 328 · Answer 11 · 2026-04-16 11:18:15

328

Views

Convergence of Truncated Expectation of Order Statistics $E[Y_{k:N}|Y_{k:N}>v]\rightarrow v$

Published on 16 Apr 2026 - 11:18

score 3.7k · Answer 12 · 2026-05-10 15:02:42

3.7k

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Maximum Likelihood Estimator of : $f(x) = \theta x^{-2}, \; \; 0< \theta \leq x < \infty$

Published on 10 May 2026 - 15:02

score 89 · Answer 13 · 2026-04-13 03:02:25

89

Views

Standardising maximum of Uniform distribution

Published on 13 Apr 2026 - 3:02

score 37 · Answer 14 · 2026-04-17 04:32:35

37

Views

Equal probability of rank implies identically distributed?

Published on 17 Apr 2026 - 4:32

score 29 · Answer 15 · 2026-04-16 03:26:33

29

Views

Probability to uniformly draw smaller than minimum/order statistic of uniform r.v.

Published on 16 Apr 2026 - 3:26

List Question

For a random sample from the distribution $f(x)=e^{-(x-\theta)} , x>\theta$ , show that $2n[X_{(1)}-\theta]\sim\chi^2_{2}$

Probabilities in Matching to the closest point

What is the probability that the inequality $Y_{(m')}<X_{(m+1)}<Y_{(m'+1)}$ will hold?

Showing that $\frac{X_{(i)}}{X_{(n)}},i=1,2,...,n-1$ and $X_{(n)}$ are independent for a population with df $F(y)=y^{\theta}$

Show that $Y_1=\frac{X_{(1)}}{X_{(2)}},Y_2=\frac{X_{(2)}}{X_{(3)}},\dots, Y_{n-1}=\frac{X_{(n-1)}}{X_{(n)}}$, and $Y_{(n)}=X_{(n)}$ are independent

Distribution of a sample IQR

A random vector of continuous random variables and its Order Statistics

Finding complete sufficient statistic

Expected maximum pairwise distance for $n$ points on a circle?

Is there an explicit expression for the density of a data point minus the sample median?

Convergence of Truncated Expectation of Order Statistics $E[Y_{k:N}|Y_{k:N}>v]\rightarrow v$

Maximum Likelihood Estimator of : $f(x) = \theta x^{-2}, \; \; 0< \theta \leq x < \infty$

Standardising maximum of Uniform distribution

Equal probability of rank implies identically distributed?

Probability to uniformly draw smaller than minimum/order statistic of uniform r.v.

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