Linked Questions
15 questions linked to/from Identity of moment-generating functions
10
votes
1
answer
17k
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if 2 random variables have exactly same mean and variance [duplicate]
If two continuous random variables have exactly the same expected value and variance, do they always have the same distribution?
- 103
20
votes
5
answers
16k
views
How is the kurtosis of a distribution related to the geometry of the density function?
The kurtosis is to measure the peakedness and flatness of a distribution. The density function of the distribution, if it exists, can be viewed as a curve, and has geometric features (such as ...
- 19.8k
26
votes
2
answers
7k
views
How would you explain Moment Generating Function(MGF) in layman's terms?
What is a Moment Generating Function (MGF)?
Can you explain it in layman's terms and along with a simple & easy example?
Please, limit using formal math notations as far as possible.
- 2,125
26
votes
1
answer
9k
views
Whether distributions with the same moments are identical
Following are similar to but different from previous posts here and here
Given two distributions which admit moments of all orders, if all the moments of two distributions are the same, then are they ...
- 19.8k
6
votes
2
answers
11k
views
Moment Generating Function for Lognormal Random Variable
I'm working through the proof of a lognormal random variable and am having some difficulty in moving through it. I understand the following:
Our CDF is $\Phi(\frac{logx - \mu}{\sigma})$, and thus our ...
- 61
7
votes
2
answers
1k
views
Is (covariance) stationarity preserved under log or exponential transformation?
In this lecture note, it (proposition 2) says that strict stationarity is preserved under transformation. However, it doesn't give the proof of this statement.
Second, what if the process is ...
- 2,611
14
votes
1
answer
2k
views
How to fit an approximate PDF (i.e.: density estimation) using the first k (empirical) moments?
I have a situation where I am able to estimate (the first) $k$ moments of a data-set, and would like to use it to produce an estimation of the density function.
I already came across the Pearson ...
- 21.9k
6
votes
2
answers
400
views
What is the famous data set that looks totally different but has similar summary stats?
There is a famous example of a collection of datasets with similar summary statistics like mean, standard deviation etc., whose visual appearances are totally different. It is named after the famous ...
- 369
6
votes
3
answers
2k
views
Can we get Moment Generating Function(MGF) from data?
We had couple of good discussions about Moment Generating Function(MGF), here and here.
But I still have questions on the applications of it and how can it be useful.
Specifically, I can understand ...
- 37.3k
3
votes
1
answer
711
views
If two distributions have the same moments, how different can they be? [duplicate]
Let us suppose we have two distribution functions $F$ and $G$ with shared domain and also shared moments but not necessarily shared moment-generating functions.
I have seen from "Whether ...
- 9,670
4
votes
1
answer
438
views
median and mean of the sample mean of i.i.d. log-normal
Let $y:=\frac1n\sum_{i=1}^n x_i$, where $\{x_i\}_{i=1}^n$ is a set of i.i.d. random variables, and every $x_i$ has a lognormal distribution $x_i \sim\text{Lognormal}(\mu,\sigma^2)$. Let $\text{Med}[y]$...
- 1,035
4
votes
1
answer
257
views
Estimate probability of event using moments of a distribution or a Taylor expansion involving the moments
Let's say we have four moments $(\mu_1, \mu_2, \mu_3, \mu_4)$ of a probabilty distribution of a random variable $X$ and the goal is to get the probability $\rm{P}(X \leq t)$ for a certain value of $t$....
- 61
4
votes
1
answer
343
views
Can the median be expressed in terms of a distribution's moments?
Given a random variable X, which (for the sake of simplicity) we'll say has some continuous distribution (whose pdf is f(x)), is it possible to express the median in terms of the distrbution's moments?...
- 492
9
votes
1
answer
507
views
Sampling from distribution known only by its moments [duplicate]
Is there an efficient, numerically stable algorithm to sample from a distribution for which we know only a certain (large) number of moments?
- 1,706
3
votes
1
answer
215
views
Finding mode using mean and skewness (and higher moments)?
I have a pdf that doesn't yield trivial derivatives, so I cannot differentiate it and find the root to determine where its max exactly occurs.
However, I have a general formula to express all its ...
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