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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.

28080 questions
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Conditions for the identity f(a)f(b)=f(a+b) to hold

If I have the identity $$f(a)f(b)=f(a')f(b')$$ for a given normalized probability distribution $f$, and additionally the constraint $$a+b = a'+b' = const.$$ for any suitable pairs of real numbers $a,b$ and $a',b'$, would this be sufficient to…
Thomas
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Are Gaussian mixtures stable?

Let $X$ be a Gaussian-mixture random vector with probability density function (PDF) $f_X(x)=\sum_{i=1}^kp_if_i(x)$, where for $i=1,2,\ldots,k$, $f_i$ is a multivariate Gaussian PDF with mean $\mu_i$ and covariance matrix $\Sigma_i$, and…
W. Zhu
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Name of Distribution Related to the Binomial Distribution

I am trying to find out if there's a standard name for the following distribution related to the binomial distribution. This distribution is basically the same as the binomial distribution, but as if the second half of the probability mass function…
GrapefruitIsAwesome
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How to combine evidence of existence vs non-existence in distance measurement?

In my scenario, I have a map of 2d points and a set of disjoint circles of radius 5 that are on the map. I'm shooting a laser beam from position (0,0) at some angle until I shoot a circle. The probability of observing the circle is 1 along its whole…
siadajpan
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What type form of CDF fits this graph?

Hi all, what kind of functional form of CDF do you think closely resembles this shape? Thanks!
user91909
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Probability distribution of the middle element for sorted three random variables

Let $x_a$, $x_b$, and $x_c$ be three random samples from a PDF $f(x)$. The samples are then sorted into $x_1$, $x_2$, and $x_3$ in ascending order. How do I get the distribution of $x_1$, $x_2$, and $x_3$? Is there a generalization for this for more…
zvxayr
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Even distribution in trapezoid

For defined in the condition of random values: The two -dimensional law of the distribution of the random vector XI = (XI1; XI2), one -dimensional laws of the distribution of the components, the vector of the average and the covalization matrix; The…
Mark
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Geometric interpretation of the distribution function for rounding errors

I need help with a part of the following question: The rounding error obtained when rounding to the nearest whole number can be regarded as a stochastic variable with uniform distribution on the interval $(−0.5, 0.5)$. Suppose you round two numbers…
frogi
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Finding 1 % quantiles from random non discrete data without sorting it

I have an array of measurements, some of those measurements are faulty, so if I do a min-max search, I get those faulty values. I'm trying to filter them out by finding 1% min and 99% max quantiles. I don't want to sort the data How can I find the…
Mich
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How do you calculate the error function for extremely small numbers?

So I wanted to find the probability (or, at least the magnitude of the probability), of something more than 70.5 standard deviations below the mean in a normal distribution. (It's nothing practical, it's just for a joke with my friends). However,…
Mewtwo 2387
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Independent and Identically Distributed and the Discrete Uniform Distribution

I am learning about IID. I would like to know from expert if it is accurate to say that the Discrete Uniform Distribution is actually an example of IID random number generator? (if is accurate to say things that way?). Second question. Wikipedia…
Marc Ourens
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Suppose $Y$ has a $Gamma (\alpha, \beta)$ distribution. Let $X = e^{Y}$. Find the pdf of $X$ and derive the mean and variance.

This is exercise 3.7.1 from Introduction to Mathematical Statistics 6th edition by Hogg, Mckean, and Craig. The question is: Suppose $Y$ has a $\text{gamma} (\alpha, \beta)$ distribution. Let $X = e^{Y}$. Show that the pdf of $X$ is given by…
mmm3
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PDF of a transformed log-uniform distributed variable

I have a random real variable $x$ with pdf $f(x;a,b)=\frac{1}{x(\ln{b}-\ln{a})}$, $0
Plagioclase
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Can you measure differences in self-similarity?

For background, I have a rudimentary understanding of self-similarity as it applies to observing network traffic as a stochastic process. I also have a robust mathematical background but not in stochastics. Assume I am looking at two different…
Will M
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Help with choosing a probability distribution to model existing dataset

I would appreciate your help with this. I have a large dataset with one variable 'days', with range 1.5 days to 23 days. Possible values are separated by 0.5 days, so the dataset only has 46 possible values. Am i right to assume that this data is…
Ren1231
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