Questions about performing probabilistic calculations, especially those concerned with the Mathematica commands Probability, Expectation and the various functions related to distributions such as NormalDistribution, CDF, PDF etc.

learn more… | top users | synonyms

1
vote
1answer
33 views

Difference in output from R's mvtnorm and Mathematica/Java

Let a=$\mathcal{N}(6.532056,0.06532056)$,b~$\mathcal{N}(8.390961,0.08390961)$ and c~$\mathcal{N}(8.736566,0.08736566)$. We use $\mathcal{N}(\mu,\sigma^2)$ notation unless specified otherwise. We ...
0
votes
1answer
497 views

PDF of binomial distribution and mixed binomial distribution

I want to plot the PDF of binomial distributed function and a mixed binomial distributed function, therefore I entered for the binomial distribution function the following: ...
1
vote
1answer
95 views

How determine The most possibility probable with programming

i have a scatter chart of probable of happen some thing like below chart link of google chart i what determine the probable The most point in below chart , can use a mathematic method to determine ...
1
vote
1answer
58 views

Stochastic Approximation and Simulation using Running Median

I have a function $$F(X_{t+1},Y_{t}^{med})= \alpha X_{t+1} + (1-\alpha) Y_{t}^{med},$$ where $$Y_{t}^{med} = Median(Y_1, Y_2,... Y_t).$$ Moreover, $Y_1 = X_1$ and $Y_t = F(X_{t},Y_{t-1}^{med})$ ...
0
votes
0answers
6 views

Probability in a knock-out tournament [migrated]

Maths newbie so please go gently. Imagine if you would: 4 teams in the semi-final of a soccer tournament A,B,C,D. A,B and C all have 20% chance of winning the tournament. D however, is the favourite ...
3
votes
2answers
85 views

Expectation of a composite Markov-Gamma distribution

In a model I have a discrete two-state first order Markov process, defined by a (2x2) transition matrix with two free parameters. If the first state occurs then the process outputs zero for that ...
4
votes
2answers
322 views

Why does this integral have a complex component?

I wanted to find the probability of my normally-distributed random variable being at least 15, so I set up this integral: ...
5
votes
1answer
137 views

Simulation Sample Paths for Stochastic Approximation Algorithm

Let $X_t$ be IID random variables in $[0,1]$ and CDF $F(\cdot)$. Suppose there exists a variable $Y_t$ given by: $Y_1 = X_1$ and $Y_t = \phi(X_t, \overline{Y}_{t-1}), \forall t >1$, where ...
7
votes
2answers
162 views

Why is mathematica giving wrong and incomparable results for the integral?

1) Integration of Gaussian Distribution with $(x,y,z)$ ranging from $-\infty$ to $\infty$ gives 1 as expected using this command in mathematica. (Total Probability = 1) $\sigma = 200000$ and ...
3
votes
1answer
95 views

Expected graph distance in random graph

I am trying to use the functionality of Expectation and Probability for random graphs, in particular for percolation models. ...
1
vote
1answer
86 views

Simulation Beta Distribution

Suppose a function such as: $\phi^{\alpha} (x,y) = \left\{ \begin{array}{l l} \alpha x & \quad \text{if $x < y$}\\ x & \quad \text{if $x = y$}\\ \alpha x + (1 -\alpha) & ...
0
votes
1answer
64 views

Integration of linked PDFs over probability simplex

I'm trying to integrate the following expression: f[a1,p1+p2+p3+p4]*f[a2,p2+p3+p4]*f[a3,p3+p4]*f[a4,p4] Where ...
0
votes
1answer
77 views

Parameter Estimation of a mixture of sums of Lognormals

Let $X$ be a random variable that is of a mixture distribution of two lognormals (with the same sigma), so $X \approx p\cdot \mathcal L (\mu_1, \sigma) + (1-p)\cdot \mathcal L (\mu_2,\sigma)$. Now ...
1
vote
1answer
78 views

Manual maximum likelihood estimation of a mixture with no closed form

Let $X$ be a random variable that is from a mixture of two Lognormals (Lognormals(mu1,sigma) and Lognormals(mu2,sigma)) and set $Y=X_1+X_2+...+X_{10}$ a sum of 10 random variables from this mixture. ...
0
votes
1answer
32 views

Using ImplicitRegion to define an ellipse around Multinormal distribution for integration

I have both a 2D 'MultinormalDistribution', and also a single xy point, and I would like to be able to calculate the probability of this point (given the multinormal distribution) and also plot an ...
0
votes
1answer
40 views

Probability of xy point on bivariate normal distribution [closed]

I have a bivariate normal distribution and I am trying to calculate the probability of finding a point at a certain distance from the mean, so far with limited success. My approach has been to build ...
6
votes
4answers
216 views
2
votes
1answer
97 views

FindDistributionParameters of a sum of a mixture distribution

I have this Mixture Distribution of two Normal Distributions: ...
0
votes
1answer
66 views

Inclusion-Exclusion Principle Implementation

I would like to know how I can write a Mathematica code for the Inclusion–exclusion principle. The formulas governing it are: $ P(\bigcup_{i=1}^n A_i)=\sum_{k=1}^n (-1)^{k-1} ...
3
votes
1answer
75 views
18
votes
2answers
270 views

Negative probability?

I am trying to get the sum of the squares of seven random variables, all uniformly distributed. This is what I tried. ...
0
votes
0answers
82 views

How to be faster at making a frequency list of increasing steps

I want to find propabilities of having a sequence in a list, by using frequencies. The case is that you will bet on an increase when the last event had an increased and bet on derease when the last ...
2
votes
2answers
111 views

Finding Expectation of function of a Log-normal distribution

Say $Y=g(X)$ and $p_X = \frac{e^{-\frac{(\mu -\log (x))^2}{2 \sigma ^2}}}{\sqrt{2 \pi } x \sigma }$ is Log-normal density function: [Wiki] Find E[Y]? Since $E[Y] = \int_0^\infty y f_Y \ dy = ...
7
votes
0answers
145 views

Calculating probabilities symbolically

Is there a way to solve for statistical quantities analytically/symbolically in Mathematica? example 1: Lets say that I want to do a calculation that requires Bayes theorem. I know p(a), p(b) and ...
4
votes
3answers
227 views

Function given exact arguments returns hugely different value than it returns when given equivalent inexact arguments

I was trying to compute the probability that a coin is from a particular underlying distribution given that a particular set of tosses was observed. (I know this can be done in a different way, but I ...
0
votes
1answer
84 views

Generating a list of standard normal random variables

Im trying to generate a list of random (standard) independent normal variables. For this, I first generate a random list of, say, 100 real numbers in the range [0, 1000], and then make them standard ...
6
votes
1answer
96 views

Why am I getting wildly incorrect results from FirstPassageTimeDistribution with inexact transition matrix?

Working on some large systems using DiscreteMarkovProcess, I changed the transition matrix to machine precision vs using exact values, which sped things up handily. ...
5
votes
1answer
333 views

Is there a free version of the Springer book “Mathematical Statistics with Mathematica”?

Is there a free version of the Springer book: $$\text{Mathematical Statistics with Mathematica}$$ by Rose and Smith ... available on the internet?
0
votes
0answers
47 views

Expectation taking unusually long to evaluate

I am trying to evaluate an expectation, but it is taking an extremely long time although the expression itself should not be too complicated. My code is ...
0
votes
0answers
40 views

Symbolic manipulation of the moments of an unknown distribution

I'm curious as to whether it's possible to get Mathematica to simplify/manipulate/expand basic expectations, conditional expectations, sums of random variables, etc. A simple example might be: ...
0
votes
0answers
33 views

Chi square: compare two different distribution

I try to compare two file with two different distribution of numbers. So i have random1.dat and random2.dat each one are vectors of more then 1000 rows. I saw from this question Doing a chi-square ...
13
votes
2answers
1k views

Obtaining joint distributions and conditional distributions using Mathematica

I have two multivariate Gaussian distributions $p(x)$ and $p(z)$ with mean vectors $m_x$ and $m_z$, and covariance matrices $\Sigma_x$ and $\Sigma_z$. my model is a simple linear model $x = W z+n$ ...
2
votes
1answer
186 views

Reversing Autocorrect, aka how to find the word that was supposed to be there

When I receive messages from people using their smartphones I usually see typos and, worst, typos corrected by Autocorrect. Now, I receive messages in English, which is not my first language. I can ...
3
votes
2answers
105 views

Calculating the conditional probability of discrete samples

I have two lists: a = {0, 1, 1, 1, 0, 1} b = {1, 0, 1, 1, 0, 0} I'd like to calculate the conditional probability of a given b; for example, $p(a=1 | b=0)$. Is ...
10
votes
4answers
513 views

How do I solve this probability problem with Probability?

Consider a stick of length 1. Pick two points uniformly at random on the stick, and break the stick at those points. What is the probability that the three segments obtained in this way form a ...
0
votes
1answer
62 views

Working with means and variances

My goal is to work out on the following equation: $$Mean(P)(1-Mean (P))\left (h + (1 - 2 h) (1 - \frac {Var (P)} {Mean (P) (1 - Mean (P))}) (1 - Mean (P)) + \frac {Var (P)} {Mean (P) (1 - Mean ...
1
vote
1answer
104 views

Bilateral Laplace Transform in Mathematica (to be used with Moment Generating Functions)?

I am trying to solve a linear ODE for a Kolmogorov forward equation to get a stationary distribution of a random variable. The easiest approach may be to transform the ODE with a two-sided Laplace ...
0
votes
0answers
41 views

Time varying Poisson rate using ParameterMixtureDistribution

I have a system in which there is a Poisson arrival process with rate $\lambda$. I need to split this process into two independent poisson processes $\lambda_i$ and $\lambda_u$. Where ...
2
votes
3answers
285 views

How do I plot two Gaussians/normal distributions with 2 different means and 2 different standard deviations?

This is probably very easy for someone with more experience, but I am trying to plot only two Normal distributions, but for some reason my Method plots 4, instead of 2. I have: ...
5
votes
1answer
100 views

MarginalDistribution with Symbolic range in ProbabilityDistribution

Given the following joint density: for 10 < x < 20, x/2 < y < x. To find the marginal density for X we do: ...
1
vote
1answer
89 views

Expressing a joint distribution for use in ContourPlot

I have $$X_1=T + W$$ $$X_2=2 T + 3 W$$ where $$W \sim N(3,5) \,\text{;}\,\, T \sim N(1,2)$$ and $$P(X=X_1)=P(X=X_2)=\tfrac{1}{2}$$ which I have awkwardly expressed as ...
3
votes
1answer
143 views

Determining the dimension of a probability distribution

Functions like Mean and RandomVariate clearly infer the dimension of the distribution passed to them. One can also usually ...
0
votes
1answer
62 views

Pattern matching with PDF, Distributed and multivariate distributions

I have defined a function to compute the Shannon entropy of a probability distribution: ent[p_] := Expectation[-Log[PDF[p, x]], x \[Distributed] p] This works ...
1
vote
0answers
57 views

An example of how to compute numerically the KL-divergence in mathematica [closed]

I wanted to compute an exact number for two probabilities that I am comparing. These are two normal distributions as: $$Normal(\mu = 5, \sigma = 4)$$ $$Normal(\mu = 5, \sigma = 5)$$ I decided to ...
3
votes
0answers
113 views

What can I do to improve the performance of my calculations?

I'm trying to express a simple probability problem in Mathematica, but am having trouble getting my calculations to execute at a reasonable speed. I have an object whose unknown location is modeled ...
3
votes
1answer
178 views

Put random points into a specific 2D subregion

I want to cover a particular subregion of the x-y plane with a random distribution. As this particular region is not a circle I encounter some problems declaring the permitted zone where to put ...
0
votes
0answers
91 views

Constrained maximum likelihood

Trying to solve a MLE with nonlinear constraints that need to be satisfied. However, the given solution do not match the constraints. Am I doing it correctly? ...
1
vote
1answer
93 views

Difficulty finding Expectation of a special function

I have a special function given as: $${\rm f}\left(r\right) ={1 \over \beta\lambda}\,2^{r/\beta} \exp\left({\left[2^{r/\beta} - 1\right]K \over \lambda}\right)$$ I should find the Expectation of ...
16
votes
2answers
761 views

How to compute the inverse CDF properly?

Note: this has been fixed in version 9. I want to compute the CDF and inverse CDF of the hyperbolic distribution: ...
12
votes
1answer
170 views

NExpectation behaves oddly with EmpiricalDistribution

Note: this is fixed in version 9. My question concerns the usage of NExpectation and Expectation and why I see the behavior I ...