A distribution is a mathematical description of probabilities or frequencies.

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25 views

Can this data be fitted with a beta distribution?

Disclaimer: I'm not a statistician but a software engineer. Most of my knowledge in statistics comes from self-education, thus I still have many gaps in understanding concepts that may seem trivial ...
2
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1answer
37 views

Why two 'modes' for a Poisson Distribution with $\lambda$ an integer?

Let $X\sim \operatorname{Poi}[\lambda]$ such that $\lambda\in\mathbb{N}$. ...
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0answers
29 views

Correlation between spatial distributions [on hold]

I would like some guidance on how best to approach the following: I have three spatial distributions (distance vs variable) each with the the same sampling interval but of different lengths ( so ...
13
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5answers
671 views

In layman's terms what is the difference between a model and a distribution?

The answers (definitions) defined on Wikipedia are arguably a bit cryptic to those unfamiliar with higher mathematics/statistics. I am a high school student very interested in this field as a hobby ...
2
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1answer
56 views

If X~Exp(λ), what is the expected value of Y=X²?

I am trying to compute this using the integral definition of expected value but I don't think I am doing it right as I am getting a very hard integral that I can not solve. When computing ...
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0answers
9 views

Distribution of same parameter estimated for many data sets

I'm using an MCMC method (http://arxiv.org/abs/1601.05388) to estimate several parameters for around 16,000 different data sets. For each data set, there is a posterior distribution on my parameters. ...
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0answers
12 views

Joint PDF of ordered statistics [on hold]

Let $Y_1 < Y_2 < … < Y_n$ be the order statistics of $n$ independent observations from a continuous distribution with cumulative distribution function $F(x)$ and probability density ...
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0answers
8 views

Statistical test between pairs of values recorded by human and machine inorder to find the agreement between them

I have a set of independent values (which are subjective) recorded based on both human observation and machine recorded ones. At this point I want to ask serval questions like what is the agreement ...
2
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1answer
19 views

How to deduct the coefficient of the Dirichlet distribution?

I am studying the textbook Introduction to Probability Models by Sheldon Ross. In Section 3.6 page 151 (10th edition), the author uses the Dirichlet distribution to deduct the coefficient of a ...
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1answer
16 views

Why is multinomial variance different from covariance between the same two random variables?

We know that if $\big(X_1,X_2...X_k) \sim multinomial(n;p_1,p_2...p_k)$ then $X_i \sim bin(n;p_i) $ Then, $var(X_i) = np_i(1-p_i)$. But we have $cov(X_i,X_j) = -np_ip_j$. So doesnt that imply ...
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1answer
34 views

Does the following pmf belong to the exponential family?

I recently saw* a pmf: $f(y)=\frac{\mu^y}{(y!)^\theta z(\mu,\theta)}$, where $z(\mu,\theta) = \sum_{i=0}^{\infty}\frac{\mu^i}{(i!)^\theta}$. * It is a bonus question on a homework assignment. My ...
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0answers
11 views

How to calculate Mean and Standard deviation in Lognormal distribution where only P90 and P10 are known

I have P90 and P10 of a lognormal distribution. P90=142.56 and P10=3415; I need to estimate the mean and standard deviation of this lognormal distribution. I have done the following steps and then ...
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0answers
20 views

Bivariate Poisson regression and Pythagorean Expectation for soccer(football) [on hold]

based on public data and using excel 2010 or after, I want to forecast/predict the football match winner.
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0answers
24 views

Can't Get a Distribution That's Reasonably Close to Data [on hold]

I've got about 30K data points. I've sampled about 1000 of them here (for reproduction's sake; I figured 1000 data points pasted here was probably a bad idea). ...
-1
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0answers
23 views

Finding the distribution and covariance matrix of a distribution

Question: Let X and Y be two continuous random variables with joint probability density function $$f(x,y)=\begin{cases}\frac{1}{2} & \text{if} \ \lvert x \rvert + \lvert y \rvert \le 1 & \\ 0 ...
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4answers
67 views

Weighted lottery

A charter school assigns seats by conducting a lottery. In the past, each child was given a number, and balls were selected randomly. This year, they are starting a new policy of giving low-income ...
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1answer
51 views

Looking for a distribution with very specific properties

I'm looking for a continuous distribution which I can parameterize such that The expected value is roughly zero The expected maximum given $x$ draws from that distribution is only very weakly ...
6
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2answers
169 views

Finding the distribution of iid variables X, Y given distribution of X-Y

Say I know the distribution of $X-Y$, but I do not know the distributino of $X$ (or $Y$), but I know that they are statistically independent, and I know they have the same distribution. Is the problem ...
1
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0answers
35 views

Can the memoryless property be applied to all probability distributions (both discrete and continuous)?

I am brand new to Cross Validated and have a question about memoryless properties on probability distributions. Here is my question, to understand how and when to apply this property of statistics: ...
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0answers
18 views

Measuring home value distribution in a city [on hold]

I would like to know how I can measure the distribution of home values in many cities. I have the following data for each city: median price in the city; number of housing units by value range, such ...
0
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1answer
20 views

Sample from a Normal-Inverse-Chi-Squared distribution

Is there a way to draw samples from the following distribution in Python? Unfortunately I wasn't able to find helpful information in the scipy help.
1
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1answer
12 views

DCC-GARCH: selection of error distribution and extraction of volatility decay

I am in a hesitation of detecting which indicators from maximum likelihood (ML) estimates of the Gaussian DCC model tell the volatility parameters' decaying. Another question is, how to know which ...
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0answers
10 views

t-ratio distribution: performing tests using the tables in Press(1969)

I obtained some t-statistics ($t_{1}$, $t_2$, $t_3$, and $t_{4}$) from a couple of OLS regressions. I want to perform tests on the variables $s_a=\frac{t_1}{t_2}$ and $s_b=\frac{t_3}{t_4}$. The ...
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0answers
15 views

Probabilities of different length and expressed genes

So let's say I have 3 different genes that I am sequencing (this means I will get a lot of fragments of each and by overlapping I can get a complete gene) them. Each gene has a different length and ...
3
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1answer
19 views

Non-central t-distributions with different degrees of freedom

I have two non-central t distributions with CDF given by $t_{n,a}$ and $t_{m,a}$ with $n>m$ degrees of freedom respectively and the same non-centrality parameter $a$. The question is: for which ...
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2answers
79 views

Is it correct? $ p(a,c|b) = p(a|c)p(c|b) $

I read two different papers on some similar problems. In one of the papers this statement is written: $ p(a|b) = \sum_{c \in C}p(a,c|b) $ While in the other it is written as: $ p(a|b) = \sum_{c \in ...
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0answers
10 views

Case control sampling - matching distribution

I have large number of observations (say few thousands) which are divided into two groups A and B. I am interested in conducting ...
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0answers
24 views

Find 95th percentile in Excel [closed]

I have data presented such as Day Approve 0 3309 1 2228 2 4449 3 5093 4 5738 5 7417 6 8408 7 8085 8 6039 9 3808 10 3463 where the Approve ...
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0answers
10 views

Subset of Pareto/powerlaw distribution

Given a set of random data generated using pareto-distribution, how can I get X% of this random data without losing pareto-distribution. In other words, how to select a subset of pareto-distribution ...
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1answer
25 views

Estimate the probability of the distribution of a sample

Suppose I have the sample of a continuous variable and I want to estimate the probability of that variable taking certain values. Suppose in addition that I estimate the density of that distribution ...
0
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0answers
44 views

If the # of people in a room is Poisson distributed, and you observe someone enter, what's the distribution of the # of people?

I hope this question is properly formulated. It's just something that occurred to me spontaneously. Consider a random variable $X$ representing some count data -- for instance, the number of people ...
3
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1answer
62 views

Does the IQR or standard deviation change when scaling or shifting non-normal data?

I'm aware that scaling or shifting data that is normal or almost perfectly normal will not significantly change the standard deviation. Through practice I've that this is not the case with non-normal ...
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0answers
29 views

Probability distribution over classes as labels in classification task

Classical classification problem has next formulation. Given a set of $n$ attributes, a set of $k$ classes and a set of labelled training instances: $(i_i, l_j),...,(i_j, l_j)$, where $ i = (v_1, ...
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0answers
15 views

posterior distribution for coin flips given uniform prior distribution [closed]

A coin has an unknown head probability $p$. Flip $n$ times, and observe $X=k$ heads. Assuming an uniform prior for $p$, then the posterior distribution of $p$ is the beta distribution $B(\alpha = k + ...
3
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1answer
55 views

How do I find the expected value of F(isher)-distribution

$E(F)=\int xf_{k,m}dx$ where $f_{k,m}(t) = \Gamma(t)=\frac{\Gamma((k+m)/2)}{\Gamma (k/2)\Gamma(m/2)}k^{k/2}m^{m/2}t^{k/2 - 1}(m+kt)^{-(k+m)/2}$. How do you find $E(F)$? Say you have to convert ...
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0answers
18 views

probability of non-exceedance or the probability of exceedance for weibull distribution [closed]

How to calculate the probability of non-exceedance or the probability of exceedance in R for Weibull distribution? R package "nsRFA" is available in order to calculate probability of non exceedance ...
2
votes
1answer
23 views

Intuitively, why is cross entropy a measure of distance of two probability distributions?

For two discrete distributions $p$ and $q$, cross entropy is defined as $$H(p,q)=-\sum_x p(x)\log q(x).$$ I wonder why this would be an intuitive measure of distance between two probability ...
3
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1answer
44 views

conjugate prior for (multivariate) Gaussian mixtures (with known mean and covariance)?

Say I have a (multivariate) Gaussian mixture model $$p(x)=\sum_k\pi_iN(\mu_i,\Sigma_i),$$ of which the $\boldsymbol\mu$ and $\boldsymbol\Sigma$ are known, so the likelihood function of the ...
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0answers
6 views

Exact sampling distribution of Cochran Q test statistic

In our course notes, it is said that the exact sampling distribution of Q in Cochran Q test can be constructed from permutation arguments. I don't know where to start.
1
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1answer
30 views

Equality in distribution [closed]

I have a problem at hand which involves showing equality of distribution and I have no idea how to proceed and what to show ultimately. Let $$\left(\matrix{U\\V}\right)\sim ...
1
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1answer
24 views

What is an “algebraic tail”?

The authors of this paper repeatedly use the term "algebraic tail" when describing some of the distributions they observed: ...the probability of remaining in a small, spatially confined region ...
1
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1answer
24 views

What exactly is a “truncated” power law distribution?

This paper describes the data they analyzed as following a "truncated" power law distribution: To me, this just looks like they multiplied a power-law distribution ($\Delta r + \Delta ...
0
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1answer
61 views

`scale` in R with no normal distribution

The function called scale, in R, does the same of subtracting the mean and dividing by the sd each element. So the scale function allows to take in count differente parameter with different scale. ...
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0answers
34 views

An asymmetrical distribution with mode at 0?

I am modelling some process where I logically want the residuals to have a maximum probability of being zero, but with more 'tolerance' towards positive residuals. So I'm looking for a distribution ...
0
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0answers
15 views

Transformation of uniform distribution

Let $X$ have the uniform distribution $U(-1,3)$. Find the pdf of $Y = X^2$. So $f(x) = \frac 1 4 $ for $-1 \leq x \leq 3$. I'm having some trouble figuring out how to do the integration in terms of ...
3
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1answer
70 views

Kolmogorov–Smirnov test vs. t-test

I'm having some difficulty in understanding the interpretation of the 2 sample KS test, and how it is different from a regular t test between 2 groups. Lets say I have males and females doing some ...
3
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0answers
31 views

Modeling distributions

Suppose I am studying a unimodal, interval-leveled variable $Y_i$ that measures e.g. individuals' positions on a (-$\infty$,+$\infty$) continuum. Then, I noticed that for different sub-categories of ...
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0answers
14 views

Upper bound for most likely category in multinomial random vector NOT being max count realized

This is a repost from a question posed at Math stack exchange: http://math.stackexchange.com/questions/1750148/upper-bound-for-most-likely-category-in-multinomial-random-vector-not-being-max Let ...
1
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0answers
20 views

Adding Normal Distributions

Let X = {32, 32, 33, 34, 35, 38, 39, 41, 41, 41, 44, 44, 45, 46, 48} (Say the scores that students got on test one) Let Y = {32, 32, 33, 34, 35, 38, 39, 41, 41, 41, 44, 44, 45, 46, 48} (say the ...
5
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2answers
191 views

Convergence in distribution of the following sequence of random variables

$X_n\sim Beta\left(\frac{\alpha}{n},\frac{\beta}{n}\right)$ with $\alpha>0$ and $\beta>0$. Does $X_n$ converges to a distribution? How do I approach to show that this converges to a ...