All Questions
Tagged with density-function marginal-distribution
6 questions
8
votes
1
answer
2k
views
The distribution of the initial point of an AR process
Consider a stochastic process $\{X_t, t = 1, 2, \ldots\}$ following the model $$X_t = \alpha X_{t-1} + e_t,$$ where $e_t \thicksim f$.
Can I say that the distribution of the initial point, $X_1$, is ...
- 333
4
votes
1
answer
1k
views
marginal conditional distribution from MCMC output [duplicate]
I have a MCMC sampler that targets $$\mathbb{P}(U_1,U_2,...U_n \mid G(U) \leq 0)$$ where $U=(U_1,U_2,...U_n)^T$. I realize now I am more interested in estimating the conditional density $$p_k = p(u_k \...
- 105
10
votes
2
answers
11k
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Problem calculating joint and marginal distribution of two uniform distributions
Suppose we have random variable $X_1$ distributed as $U[0,1]$ and $X_2$ distributed as $U[0,X_1]$, where $U[a,b]$ means uniform distribution in interval $[a,b]$.
I was able to compute joint pdf of $(...
user1102
6
votes
1
answer
391
views
Question about a marginal distribution
If I observe the following:
$X \sim N(\mu_x,\sigma^2_x)$
$Y|X=x \sim N(x,\sigma^2_y)$
My objective is to calculate the marginal distribution of $Y$.
(Since the variance term does not address some ...
- 1,113
4
votes
0
answers
729
views
Constructing a joint distribution from pairwise bivariate marginal distributions?
It's fairly well-known that given univariate distribution functions $F_X, F_Y, F_Z$, one can construct the joint distribution $F_{(X, Y, Z)}(x, y, z) = C(F_{X}(x), F_{Y}(y), F_{Z}(z))$, where $C$ is ...
- 385
4
votes
2
answers
1k
views
Interpretation of cartesian product of the support of marginal distribution
Suppose we have a multivariate data set, $s = (s_1, s_2, ... s_p)$ and each $s_i$ is distributed with a distribution that has finite support (we'll call each $s_i$ a "source"). Let us ...
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