Questions tagged [probability-or-statistics]

Questions about systematic data collection and organization, or the application of probability theory to model the inherent patterns and properties of sampled data, underlying data distribution(s) or random processes.

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1answer
77 views

Simplifying / approximating compound negative binomial - binomial distribution

Suppose we have that the distribution of a count $x$ is given by a binomial distribution: $x\sim \mathcal{B}(n,\theta)$. Further, suppose that the sample size $n\sim NB(\lambda,\kappa)$, where this ...
3
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2answers
77 views

Estimation of the expected Euclidean distance between two random points on a unit $n$-hemisphere

What is the best approach to estimate, with Wolfram Mathematica, the expected Euclidean distance (in a $(n+1)$-dimensional space) between two points selected uniformly at random on a unit $n$-...
2
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3answers
84 views

Estimate the expected distance between two random points on the unit $n$-sphere [duplicate]

What is the best approach to estimate, with Wolfram Mathematica, the expected Euclidean distance in a $(n+1)$-dimensional space between two points selected uniformly at random on the unit $n$-sphere? ...
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1answer
29 views

How to find the inverse of CDF of geometric function? [closed]

The cdf of geometric distribution is given by $ F(x)=1-(1-p)^x$. I want to calculate the inverse of it, for example, $F^{-1}(U)$ I am doing the following ...
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2answers
64 views

TransformedDistribution of normal and skew-normal distributions

I have the following distributions: distC =NormalDistribution[251.563, 0.317394] distS =SkewNormalDistribution[252.973, 0.503173, 5.59741] I want to analyse what ...
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0answers
58 views

Solving $E[abXab]=Y$ for Gaussian $(a,b)$

I have $d/2$-dimensional variables $a,b$ jointly distributed as Gaussian($\mu,\Sigma$) in $d$ dimensions, and need to solve the following equation for $X$ $$E[ab^TXab^T]=Y$$ This is equivalent to ...
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1answer
42 views

Implementing Random process for exponential correlation function

I'm trying to simulate a random process for a variable $-1<X(t)<1$ with average 0, i.e., $\left\langle X(t)\right\rangle =0$ and correlation $\left\langle X(t)X(0) \right\rangle \propto e^{-t/\...
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0answers
20 views

Consistency of sample quantile to population quantile for discrete variables [closed]

Can I know if the sample quantile converges to the population quantile in probability for discrete variables? If we use Hoeffding (1963)'s results, is this true?
3
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1answer
69 views

Evaluating expected improvement in Mathematica

There is a concept in optimization called expected improvement where you sequentially search for the value of x that optimizes the problem. Here is a screen shot of the general idea of the derivation: ...
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1answer
81 views
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1answer
156 views

How to plot this pdf

Let $x\sim N(\mu,\sigma^2)$ and $y=\max\{e^{x-1}-\kappa,0\}$. How to get and plot the pdf of y? In particular, there will be a probability mass at $y=0$, which is a nondifferentiable point. I tried <...
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1answer
79 views

How to solve the Summation equation by FindRoots [closed]

I want to find out the value of alpha and lambda where u lies between 0 and 1.
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2answers
144 views

Raising the normal distribution curve to a specified height on the $y$-axis

I'd like to know how to fit the normal distribution curve between $x$ and $y$ values so that the curve maintains its bell shape. I guessed the sigma is the scale ratio, but it doesn't work as I ...
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1answer
41 views

Defining a Gaussian mixture distribution for $N$ number of Gaussian distributions

I am experimenting a bit with mixed-Gaussian distributions. If I want to define a mixture of two or three distributions, I do this with: ...
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2answers
43 views

using exponential distribution to solve a half life problem [closed]

i have information about the half life of a certain element. the half life is 29 years. i need to calculate how much of this material is left if we start counting from 1954, which was 66 years ago. i ...
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1answer
103 views

Is it a bug in TransformedDistribution?

I worked with ...
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3answers
340 views
2
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1answer
71 views

trying to solve for mean and standard deviation using Normcumdist and Solve [closed]

I am trying to find values for the mean and standard deviation of a normal distribution with these characteristics. $\qquad P(X \le 90) = 0.96$ $\qquad P(X \le 50) = 0.3$ I am trying to do this using <...
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0answers
42 views

Find custom distribution parameters that best fit the PDF/CDF data histograms

I have the probability and cummulative density histograms of some data. I need to find the parameters of a custom distribution that best fit the data. For probability distributions included in ...
1
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1answer
126 views

Evaluate 3D- and 5D-constrained integrals for absolute separability probabilities

In a recent posting, TwoQubits user JimB, employing a change-of-transformations put forth by N. Tessore, was able to confirm a formula for the "two-qubit absolute separability Hilbert-Schmidt ...
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0answers
40 views
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2answers
49 views

How to make calculations involving symbolic summation?

I want to minimize a function involving the sum of $n$ fixed (but indetermined) $x$ values, for example: Minimize[Sum[(x[i] - a)^2, {i, 1, n}], a] Expected answer: ...
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1answer
25 views

multivariate Gaussian distribution with identity covariance

I want to draw Geometry (or contours) for multivariate Gaussian distribution with identity covariance matrix (or draw decision boundary). How this is possible via Wolfram's online at Here? Please ...
2
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0answers
35 views

Failure in MultinormalDistribution

My RandomVariate fails to evaluate when sampling from a multinormal distribution, any idea what's happening here? This is Mathematica 12.1 on Mac: ...
2
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3answers
85 views

What is the probability of the digit $k$ in the number $x^n$

Well, the title of the question says it all: how to write a code that finds the probability of the digit $k$ in the number $x^n$? For example, when $x=2$, $n=100$, and $k=7$ we are trying to find how ...
3
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3answers
368 views

Calculating Variance (without Variance expression)

I am learning Mathematica on the fly, one of my tasks is to find the variance of white noise. I followed the tutorial for finding white noise by using the code: ...
1
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1answer
95 views

Fisher information for a Gaussian [closed]

I would like to calculate the Fisher information for $f(x|\alpha)=\frac{1}{(2\pi \delta^2(\alpha))^{1/2}} Exp\{-\frac{(x-\mu(\alpha))^2}{2\delta^2(\alpha)}\}$ using ${\rm FisherInformation}[\{\mu, \...
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1answer
48 views

Fisher distribution expressed with Chi ²

I am learning about the ANOVA test. This involves the Fisher-distribution. I know there is the ANOVA function and the ...
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0answers
28 views

Speed up exact distribution of the sum of the top $k$ statistics on a bounded discrete uniform distribution?

I came across a nice answer by Sasha (I believe a Wolfram engineer) on mathematics stack exchange regarding the distribution of the sum of the top $k$ order statistics. (This was an answer to an RPG ...
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5answers
323 views

If someone would want to think about the question: mathematical-optimization “Banknote”

I solved the puzzle of IBM Ponder This September 2019 by my code written with mathematica. I would like to share this code after the solution that will come as soon, and discuss it. In the meantime, ...
6
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4answers
1k views

Mean age of people [closed]

I have the following datas: I want to find mean age by using following formula, Any way to do this in general in Mathematica easily.
2
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1answer
55 views

Intepreting the results of DistributionFitTest, and other alternatives in Mathematica 12.1

I have been playing with DistributionFitTest as a means of testing how normal some data sets I have. I've been working with some simulated data sets so I can try ...
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0answers
40 views

Computing the Mean of Around Values

I understand the computation of the uncertainty of independent Around values to be based on the following first order approximation $$ \delta f(x,y)=\sqrt{\left(\frac{\text{$\delta $f}}{\partial x}...
1
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1answer
64 views

i need to simulate a roulette table where a perosn bets $10 on red 1 time, 5 times,20 times, 100 times and 10,000 times

I need to simulate a roulette table where a perosn bets $10 on red 1 time, 5 times,20 times, 100 times and 10,000 times, i then need to find out how much the person wins or loses once they play 10,000 ...
1
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2answers
172 views

Confirm and possibly simplify a 2009 result for a 2D constrained integration

This is a direct descendant of two other recent questions, 3D and Equivalence, both of which have been answered in skillful, interesting manners. (See also the comment [actually answer] of JimB to ...
3
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2answers
565 views

How can I make an animated demonstration of the Wigner semicircle distribution?

With Mathematica 10, it's possible to draw the semicircle distribution of R. Wigner: ...
3
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3answers
117 views

How to simulate the roll of 3 or more dice and ask for a sum of 3 or more?

How to simulate the throwing of 3 or more dice and ask for the sum of 3 or more and indicate the number of calves, or more that are produced. For example if you throw 3 dice, how many cases will add ...
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0answers
45 views

Mann Whitney Test

I am trying to check data in Mathematica with the Mann Whitney Test. The author states: Mann–Whitney's U-test; U = 609, z = 2.07, p < 0.05. How would I put this ...
1
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1answer
55 views

Generating a set of random variates from Poisson distribution

Say I am not allowed to use built-in PoissonDistribution, which means I should generate 100 random numbers first, and then with these 100 random numbers to generate 100 random variates from Poisson ...
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1answer
60 views

Expressions for moments of sample cumulants?

I sample $n$ points from standard normal and need the mean and variance of 3rd and 4th sample cumulants. @JimB suggested that variance of 4th sample cumulant is given by the expression below. This ...
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1answer
53 views

Can the WishartMatrixDistribution command be used for generating random density matrices?

I am interested in generating random members of two classes of $n \times n$ positive-definite matrices $A$ and $B$--the former symmetric in nature, the latter, Hermitian. The standard (Ginibre-matrix-...
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0answers
36 views

Piecewise function inside ProbabilityDistribution causing errors

I'm using a complicated Piecewise function to create a probability distribution and draw random points from it. ...
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1answer
49 views

How to emulate statistical command choice tab of this widget?-how to do what i ask?

I designed this little program, but I want you to be able to choose what I want to look for by choosing it as you do with the widget tab, please help me. widget Widget of internet my program ...
1
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1answer
46 views

Probability distribution with random paremeters

Is it possible to set something like this? A probability distribution with random parameters ...
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0answers
28 views

Unable to evaluate expectation of sum, but able to evaluate expectation of each summand

I would like to evaluate the expectation of the expression x + x Log[x] where x follows a generalised gamma distribution ...
2
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1answer
82 views

Turning a matrix matrix into a probability table

I want to build a probability table that is able to answer questions such as "if i roll 5, 4 sided dice what is the probability i get at least a 16?" My current code is: ...
6
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2answers
73 views

Ideas to speed up an order statistic calculation?

A toy example: {n, top} = {25, 100}; mxs = RandomReal[{0, top}, n]; dist = UniformDistribution[Thread[{0, mxs}]]; result = Mean[OrderDistribution[dist, n]] With ...
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1answer
57 views

Problem plotting expression involving Generalized hypergeometric functions $_2F_2 \left(.,.,. \right)$

I'm trying to plot a graph for the following expectation $$\mathbb{E}\left[ a \mathcal{Q} \left( \sqrt{b } \gamma \right) \right]=a 2^{-\frac{\kappa }{2}-1} b^{-\frac{\kappa }{2}} \theta ^{-\kappa } \...
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0answers
32 views

Adding a module to teach Mathematica the Laplace transform of particular Mittag-Leffler functions

Mathematica 11.3 is not aware of a useful Laplace transform LaplaceTransform[t^(-a) MittagLefflerE[a, a, t^a], t, s] which for ...

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