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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The problem of finding the maximum coefficient term in the binomial expansion,Find the value range of K
The problem is shown in the figure, and the result should be the range of K obtained at the end of the image
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3
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How to find the K value in the probability inequality of binomial distribution?
dist = BinomialDistribution[100, 1/3]
Solve[{PDF[dist, k] >= PDF[dist, k - 1],
PDF[dist, k] >= PDF[dist, k + 1]}, k] // FullSimplify
In this binomial ...
- 1,373
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Quickly simulating "mean-time until collision"
Edit high-level summary of problem/solutions in Mathematica community post
Suppose I draw (with replacement) $k$ colored balls from bins with probabilities $h_1,\ldots,h_d$ until some color is drawn ...
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Mapping a vector to a unique number using statistical coefficients and vice versa [migrated]
Working with sequences of various dimensions of random integers, I saw that Wolfram Alpha provides information on a number of statistical indicators for this sequence.
Among these indicators, for ...
- 2,344
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Work-arounds to InverseFunction not evaluating?
Inverse CDF of Marchenko Pastur fails to evaluate at seemingly random points as you can see below. Is there an easy workaround?
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Non-uniform birthday problem in Mathematica
Suppose my year has $d$ days. I have a vector of probabilities of being born on those days as $h=p_1,\ldots,p_d$, and want to estimate the smallest $k$ such that probability of of birthday collision (...
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FindDistribution analog: automated data modeling with all Wolfram statistical distributions
BOUNTY GOAL
To get bounty I am asking to build a function that serves as an analog of FindDistribution. You can also simply re-implement ...
- 69.8k
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Get All Discrete Univariate Distributions with Symbolic Parameters
I am trying to get all Discrete Univariate Distributions with symbolic arguments from any place in Wolfram Language system. For example this guide:
http://reference.wolfram.com/language/guide/...
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How to find this probability?
I am solving a problem from 17th Kolmogorov competition.
Let $X_1,X_2,\dots,X_{50}$ be IID discrete random variables s.t.
the probability of $X_1=-1$ equals $\frac 1 9$, the probability of $X_1=- \...
4
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4
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242
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Incorrect results of Mean and Variance of TransformedDistribution
I am solving a problem from 17th Kolmogorov competition.
Let $(x,y)$ be a Gaussian random vector with mean $(0,0)$ and a covariance matrix $$\left(\begin{array}{cc} 1&r\\r&1\end{array} \right),...
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Measurement error propagation onto fitting-parameters
I have a dataset consisting of (t,y) Tuples, where each y has a known measurement error (standard deviation). I would like to fit a trapaze-function into the data and obtain the fitting paramaters and ...
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Expression for variance of a truncated distribution as a function of the point of truncation
I am working on a project where I need to calculate variance of a truncated distribution. Suppose $X$ has some distribution and $x\in\mathbb{R}$. I am interested in $var(X|X\leq x)$. Given some ...
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Moment problem for a discrete probability distribution
Is there an elegant way to use Mathematica to find entries of a discrete probability distribution $\{p_i\}$ by using a finite number of calls to $m(t)=\sum_i p_i^t$?
There's a wikipedia article on ...
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Mathematica unable to realize simple distributional relationship
I was trying to find the CDF for the following problem:
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Why the difference in these results of estimating the parameters of Erlang distribution?
Investigating (in 13.2 on Windows 10) the FindDistributionParameters command for learning purpose, I consider
a small sample ...
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4
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Speeding up Gaussian sampling
Edit Greg Hurst answers show how to independently get 3x speed-up using single-threaded MKL implementation and 4x speed-up by using native implementation with multi-threading, can they be combined?
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How to find the regression line equation of these two groups of data and draw the scatter diagram and regression line?
These two sets of data are as follows:
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Why isn't that conditional expectation calculated directly?
I mean
Expectation[y \[Conditioned] x/y == t, {x \[Distributed] ExponentialDistribution[2],
y \[Distributed] ExponentialDistribution[3]}]
returns the input in 13....
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2
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91
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Help regarding an integral in about certain probability [closed]
In the following $V$ is an uniform variate in $(0,1)$ ,$T$ is another independent random variable with CDF $t^{n-1} $and $u>1$ is a parameter.A friend sought help in an assignment in the ...
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How to calculate the number of prime numbers in a group of numbers?
If two different numbers are randomly selected from seven integers from 2 to 8, what is the probability of the two numbers being mutually prime?
Take 2 different numbers randomly from 7 integers from ...
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How to Find a Weighing Matrix of Size n?
Weighting matrices appear in the statistical design of experiments (Weighting Matrices and Statistical Design of Experiments.
A weighting matrix is a generalization of Hadamard matrices, e.g.,
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Is it normal that adding constraints on the parameters of NonlinearModelFit increases execution time 100 times??
Normally, reducing the optimization domain by adding constraints should reduce the time of execution. In my case however, this puts the NonlinearModelFit in a coma. Without constraints, 8 seconds ...
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Can constraints on the parameters be imposed in NonlinearModelFit? [closed]
Hi I cannot figure out this from the documentation of this command. For example, take one of the examples in the documentation, where I also added initial guesses for the parameters.
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How to define a multivariate region of space on which to minimize a function?
My objective is to optimize a function that takes two vectors as argument: a parameter vector of probability to be optimized on, and the input data.
In other words am trying to tell Mathematica that ...
- 185
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Was there ever a package called "BinThis"?
I'm working my way through someone's old code and rebuilding it.
In one of the notebooks it appears they used a package called "BinThis" which I cannot seem to find any documentation for or ...
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27
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0
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1
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89
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How to plot a hazard function?
I would like to plot a hazard function when the CDF and PDF are not in the closed form. The PDF and CDF are given below
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1
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54
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How to Chi-square test in statistics? [duplicate]
Can we be 99% sure that there is a difference between the health habits of the group suffering from the disease and the group not suffering from the disease? The calculation formula and data are shown ...
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How to calculate that conditional expectation?
I mean the expectation of x*z under the conditions (y + z == 8) && (z*w == 2) && (w + y == 1), where ...
3
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1
answer
79
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Calculating a conditional expectation
Suppose that $X$ follows a beta distribution with parameters $\alpha > 0$, $\beta > 0$. I want to calculate
$$\frac{\int_c^1 x f(x) dx}{P(X \geq c)} - \frac{\int_0^c x f(x) dx}{P(X \leq c)}$$
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106
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53
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Standard Deviation of Non-Rectangular Array
I have a list of about 700 smaller lists, most with different dimensions. They range from 1 element to 18 elements long.
Think like:
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Specific Fox H-function becomes a constatnt function
The Fox H-function
FoxH[{{{1/3, 2/3}}, {{1/2, 1/2}}}, {{{0, 1}}, {{1/2, 1/2}}}, x]
has the same numerical value, 0.431029, at an arbitrary x value.
This specific ...
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Probability of a point being from the same distribution as sample [closed]
I have a sample of two-dimensional points {{x_,y_1},..{x_n,y_n}}, I've built a linear regression line, there seems to be a correlation between X and Y (Pearson's 0.662 if that matters).
Now what I ...
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Express the PDF of StableDistribution in terms of FoxH for the case of alpha values grater than 1
The PDF of StableDistribution in terms of FoxH for the case $\alpha\leq 1$ is available at https://reference.wolfram.com/language/ref/FoxH.html namely
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1
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Use Mathematica to solve equation derive the probability distributions using the Principle of Maximum Entropy
I am reading the article Deriving probability distributions using the Principle of Maximum Entropy and trying to derive some of the equations in it automatically using Mathematica.
I want to solve the ...
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Use Mathematica to derive the probability distributions using the Principle of Maximum Entropy
I am reading the article of Deriving probability distributions using the Principle of Maximum Entropy
and I am trying to derive some of the equations in it automatically using Mathematica.
1. ...
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Calculating Percentile of a data set [closed]
Can anyone help me how to compute 25$^{\text{th}}$, 50$^{\text{th}}$, 75$^{\text{th}}$ and 90$^{\text{th}}$ perecentile of a dataset.
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I want to increment the data one by one so that the histogram changes in Manipulate
BarChart[{1,2,3,4,5,6,7,8,9}]
How can I pre-populate the data from this source code and move it with Manipulate to show how the ...
user89156
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Conditional Expectation of an autoregressive (AR1) Process
Suppose X is a time series that follows the process:
$X[t]=\rho X[t-1] + \varepsilon[t]$
where $\varepsilon[t] \sim \mathcal{N}(0.0, \sigma)$, $\varepsilon[t]$ is IID and $X[0] \sim \mathcal{N}(0.0, \...
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Solving a system of equations with distributional constraints
I'd like to generate samples of real numbers respecting distributional constraints. I tried (here, for a sample of 17 reals):
...
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131
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Incorrect result of ParameterMixtureDistribution
Let us consider in 13.1 on Windows 10
...
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0
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28
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Repeatedly sampling posteriors for Bayesian inference + convergence
I start with some prior, $\Theta$, with PMF $f_{\theta}(\theta)$. $\theta$ is the probability of an event, $X$, yielding a success. Then, I use Monte-Carlo simulation to sample a $\theta$ from $\Theta$...
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Binomial distribution where probability parameter is also a distribution
Suppose I have $J \sim$ Bin$(25, P)$, but instead of having fixed $P$, I have a known PDF for continuous $P$, given by $f_{P}(p)$. How would I find $\mathbb{E}[J]$, given this to be the case?
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Computing First Moment of TransformedDistribution slow. Is there a way to speed things up? If not, can you help me understand why its slow?
I'm a novice Mathematica program, toying with the idea of solving for the first four moments of a linear combination of a multivariate Gaussian mixture distribution. The first two moments I have ...
2
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2
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106
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Infer Parameters of LogNormalDistribution
I am trying to explore whether Mathematica can help me infer the parameters of a LogNormalDistribution from observing the values of some integrals. For example, I ...
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85
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How to sample from a `MultinormalDistribution` with a positive semidefinite covariance matrix?
I'm trying to sample from a Gaussian process (GP) following these tutorials:
https://peterroelants.github.io/posts/gaussian-process-tutorial/#Sampling-from-prior
https://stephens999.github.io/...
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QQ plot with confidence intervals
How do I plot a QQ plot with confidence interval bands? QuantilePlot does not seem to have an option to do this. This is easily done in R. Thanks in advance.
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