2
votes
1answer
46 views

FindDistributionParameters of a sum of a mixture distribution

I have this Mixture Distribution of two Normal Distributions: ...
5
votes
1answer
291 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?
5
votes
1answer
94 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
84 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
137 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 ...
3
votes
1answer
193 views

Categorical Distribution

Suppose I want to do calculations with a random variable $X$ that has a simple categorical distribution (a.k.a generalised Bernoulli distribution or discrete distribution). I was expecting to be able ...
0
votes
1answer
109 views

PDF for Gamma Distribution not what I expect

I have plotted the the PDF for a Gamma Distribution with various parameters (e.g. 3 and 5) using Manipulate: ...
4
votes
1answer
78 views

Define customised distribution with discontinuous CDF

I have the following CDF: ...
0
votes
0answers
43 views

Using an Interpolating Function as a probability density function [duplicate]

I have seen a couple of similar questions but have not been able to figure out a solution for my particular problem. I have a probability density function of two variables ...
1
vote
0answers
201 views

When are `If`, `Piecewise`, `Switch`, and `Which` interchangeable and when are they not?

Experimenting with joint dependent distributions via the TransformedDistribution function, I used the following to derive a distribution where the second variate is ...
7
votes
1answer
122 views

How to create a spliced survival statistical distribution?

I am trying to use Mathematica for more of my reliability engineering work and am having trouble using SplicedDistribution. I have a Weibull distribution (dist1) associated with a low stress ...
0
votes
1answer
184 views

Solve Probability of Distribution

Why does this work: Solve[Probability[x <= t, x \[Distributed] NormalDistribution[]] == 0.95 ,t] But this doesn't: ...
4
votes
2answers
131 views

Finding the characteristic function of a TransformedDistribution[]

I am trying to find the characteristic function of a sum of "named" distributions, though I am interested in how to use Mathematica to find the characteristic function of $$f(X_1,\ldots, X_n),$$ where ...
6
votes
1answer
144 views

RandomVariate does not fill range of PDF of distribution

I've declared my own probability distribution as follows dist[a_, b_] := ProbabilityDistribution[Cos[(b x)/2]^2 Sinc[a x]^2, {x, -400, 400}]; When I try to ...
4
votes
4answers
129 views

How do I emulate DiscreteUniformDistribution in Mathematica?

How do I define a function from scratch that emulates DiscreteUniformDistribution? As shown below, attempting to use ...
0
votes
1answer
453 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: ...
0
votes
1answer
146 views

How to simulate with a user specified bivariate continuous probability distribution [duplicate]

I am very new to Mathematica set up and I have the following question: I have a bivariate probability distribution which is a little complicated and of the form: $$f(x,y)=(a_0+a_1+a_2)\frac{a_1 ...
2
votes
3answers
262 views

Covariance of transformed random variables

I am trying to solve the following: $\begin{align*} &X \sim N(1,1)\\ &\mathrm{cov}(X, X^3) = \text{?} \end{align*}$ where $\mathrm{cov}$ is the covariance. How would you do this in ...
0
votes
0answers
128 views

Plotting a mixture CDF with a truncated distribution in version 7

I'd like to plot the CDF of the following pdf in Mathematica 7: $$f(x)=0.1 g(x)+0.85 m(x)+0.05 h(x)$$ where $$ \begin{array}{ccl} g(x)&:&P(0)=1,\ P(x\neq 0)=0\\ ...
1
vote
1answer
188 views

Safe values of $\mu$ and $\sigma$ when randomly sampling from a Log-Normal Distribution?

I believe I'm obtaining overflow errors when randomly sampling from a log-normal distribution with the command: RandomVariate[LogNormalDistribution[μ, σ], 1] ...
2
votes
0answers
523 views

Calculate variance of random walk?

How can I symbolically calculate the variance of the following random walk in Mathematica? Given several discrete random variables such that $p(Z_i=1-2k)=p$, where $k$ is a small real number, and ...
0
votes
1answer
709 views

Solving derivative of cumulative normal distribution log likelihood

I am a newbie and I'm trying to use Mathematica to obtain the symbolic Maximum Likelihood Estimation for a cumulative normal distribution. So far I have reached the step where I have the derivative of ...
4
votes
3answers
549 views

Graphical Plots of PDF and CDF

I have a joint density and distribution function that I want to plot in a meaningful way, (i.e., want to be able to see how the functions behaves as changes in x and y happen simultaneously. If ...
4
votes
1answer
161 views

Expectation of CauchyDistribution

I've noticed this strange behavior and I'm wondering if it's a bug. I define a Cauchy distribution: c = CauchyDistribution[0, 1]; If I evaluate ...
13
votes
1answer
335 views

RandomVariate returns values outside the support of a PDF

Let $X$ be a random variable with pdf: dist = ProbabilityDistribution[1/(Abs[x]*Log[Abs[x]]^2), {x, -E^-2, E^-2}] Here are some pseudo-random drawings from it: ...
0
votes
1answer
227 views

Trying to plot this probability

Can anyone help me plot this? log P(X >= x) = alpha logx x=0.001 + k(0.001) k= 0, ..., 100 I can't figure out the coding for this.. I've been trying this for a while, and can't seem to figure it ...
9
votes
3answers
2k views

How to generate a RandomVariate of a custom distribution?

I'm trying to generate a pseudorandom variate out of a custom distribution. Suppose I want define a custom distribution, and for the sake of simplicity I define a Poisson distribution (the ...
16
votes
2answers
732 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: ...
13
votes
2answers
975 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 $x = W z+n$ ...
7
votes
1answer
832 views

Probability and distribution from actual data

Let's say I have some data from a real world system: ...