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Results tagged with normal-distribution
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user 27403
The normal, or Gaussian, distribution has a density function that is a symmetrical bell-shaped curve. It is one of the most important distributions in statistics. Use the [normality-assumption] tag for asking about testing for normality.
5
votes
Accepted
Is there a numerical solution to a mixture model of two normal distributions?
The approach depends on whether the sampling data includes or not an indicator variable that specifies from which normal distribution each observation is issued.
If the data includes this indicator v …
- 4,146
4
votes
Accepted
Probability of Largest Sample Observation
There is just a small mistake in the development provided in the question. The mistake comes from the fact that
$$
P(Y > y) \neq P(X_1 > y) \cdot P(X_2 > y) \cdot P(X_3 > y) .
$$
Here is a way to solv …
- 4,146
5
votes
Confused about meaning of rule
The notation '$X_k \in N(\mu,\sigma)$' in your source means that the random variable $X_k$ has a normal distribution with mean $\mu$ and standard deviation $\sigma$. The second symbol in $N(\cdot,\cdo …
- 4,146
1
vote
Normal curve probability mean
Since the question is flagged as self-study, I'll just provide some hints to (hopefully) help you derive the solution. I'll amend/complete my answer based on your progress.
As a starting point, you m …
- 4,146
6
votes
Accepted
Determining the probability of $X_2 \ge X_1$ given they have different probability functions
Assuming that random variables $X_1$ and $X_2$ have joint density $f_{X_1, X_2}$ and marginal densities $f_{X_1}$ and $f_{X_2}$, we have
$$
P(X_1 \leq X_2)
= \int_{-\infty}^{\infty}\int_{-\infty}^{x …
- 4,146
27
votes
How to simulate from a Gaussian copula?
There is a very simple method to simulate from the Gaussian copula which is based on the definitions of the multivariate normal distribution and the Gauss copula.
I'll start by providing the required …
- 4,146
3
votes
How to prepare variables with mild skew for multiple regression?
If you're looking for a transformation of the data, you might want to consider the Box-Cox transformation which is reviewed in this article.
- 4,146