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Questions tagged [probability-distributions]

Questions on using, finding, or otherwise relating to probability distributions, probability density functions (pdfs), cumulative distribution functions (cdfs), or other related functions. Use this tag along with the tags (probability), (probability-theory) or (statistics).

Any probability distribution, including beta, binomial, chi, Erlang, gamma, geometric, lognormal, negative binomial, normal (Gaussian), Pareto, Poisson, Student's t, uniform, Wald, Weibull, zeta, and Zipf.

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Is it true that $\lim\limits_{x\to\infty}{x·P[X>x]}=0$?

I ask this because I'm trying to understand a proof of the expected value of a non negative random variable is equal to $\int_{0}^{\infty}(1-F(x))dx$ ($F$ is the distribution function of $X$) when $E[X]$ exists, and in some step I have…
Aarón David Arroyo Torres
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Inverse gamma vs Pareto distribution

What is the physical difference between inverse gamma and Pareto distribution. Which of them is more heavy tailed? To be precise, since both of them are heavy tailed, mean of both are defined for $\alpha>1$ and variance for $\alpha>2$. Their CDF…
shaifali Gupta
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How to use the joint distribution of X,Y for the distribution of X+Y with unknown dependency structure

Currently I'm reading a paper about model uncertainty and Value-at-Risk aggregation. The goal is to calculate boundaries for $VaR_\alpha(X+Y)=F^{-1}_{X+Y}(\alpha)=inf\{m|\mathbb{P}(X+Y+m<0)\leq\alpha\}$ with unknown dependency structure, so we don't…
Leoncino
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Why is the distribution of mean firing rates of a neuron Gaussian?

I'm reading "Principles of Neural Information Theory" by James V Stone and in section 3.5 he says that the distribution of firing rates (of a single neuron) is generally assumed to be approximately Gaussian. He proceeds to give a mathematical…
Eben Kadile
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What is the distribution created by this?

So I have a group of people. Each of them is 60% likely to vote on A and 40% likely to vote on B. What type of distribution does this create if I'm looking for amount of people that vote on A - the amount of people that vote on B? I'd say it would…
huB1erTi2
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How did we know that this distribution is triangular and symmetric about 0?

I know that this distribution is symmetrical about y axis since f(-x)=f(x) but how did we know that it was symmetrical about 0 an dthat it is a triangular distribution? Since I know that a triangular distribution has the following expression: And…
Rayri
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Entropy of a unimodal continuous probability distribution

Among unimodal continuous probability distributions supported on the positive reals and whose mean and mode coincide, which one has the maximal entropy ?
Sylvain Julien
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how to calculate mean and variance for logistic distribution

I need to have a formula for calculating the mean and variance for logistic distribution to fit some data I have to it. I know that the mean is $\int_{-\infty}^\infty xf(x).dx $ where f(x) is the pdf for the distribution which is…
Hassan
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Intuition behind expected value in a geometric distribution

I'm trying to gain a better intuitive understanding of the expected number of failures before the first success. My current understanding is that in a geometric distribution where the probability of success is p, the expected number of trials up to…
Anonymous
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Exponential Probability distribution

People getting to a builduing in time gaps that distribute exponential, in 3 people per minute rate. let X be the rate of people that entering the building. X~exponential(3). What is the probability for the 3rd person to get to the building in less…
adamco
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Find the probability for $T_x>T_y$ given densities?

I don't understand how to find the probability $P(T_x>T_y)$, when we know that $f_{T_x|T_y}(x|y)$ is $exp\left(\frac{1}{y}\right)$ and $f_{T_y}$ is $exp(\beta)$. I would do this to start with: $$P(T_x>t|T_y=t),$$ but I cannot use condtitional…
Frederik
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Sampling from a uniform Dirichlet distribution

I'm trying to get a sample of points distributed uniformly in the 26-dimensional simplex (otherwise put, uniformly distributed 27-dimensional probability vectors). As I have been told, for example, here, the right way to do this is to sample from…
Schiphol
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Questions about limits to find a pdf

I have a question about the following example (please see image). I fully understand the theory on how to find a pdf from a cdf and everything else, but the only thing I cannot seem to comprehend is how they determine the integral limits. If the…
MathNoob123
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PDF of joint multivariate normal distribution

I'm trying to understand what this means: $\mathcal{P}(\boldsymbol{\mathrm{s}}|\boldsymbol{\mathrm{r}}, A) = \int_{-\infty}^{\infty} \cdots \int_{-\infty}^{\infty} …
Bernd Wechner
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Joint Distribution Function

Hi Guys, Just need help understanding how to go about doing this question. I know how to convert single distributions but I'm unsure about how to do the joint ones. I usually draw a diagram representing the region I need to calculate but don't know…
Ricky Rozay
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