Linked Questions
15 questions linked to/from Whether distributions with the same moments are identical
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Example of random variable with a unique moment sequence but mgf DNE in a neighborhood of 0 [duplicate]
Do you have an example of a random variable $X$ with a unique moment sequence but whose mgf does not exist in a neighborhood of 0?
In other words, I'm looking for a counterexample to the converse of ...
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Does mean=mode imply a symmetric distribution?
I know this question has been asked with the case mean=median, but I did not find anything related to mean=mode.
If the mode equals the mean, can I always conclude this is a symmetric distribution? ...
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Does mean = median imply that a unimodal distribution is symmetric?
For a unimodal distribution, if mean = median then is it sufficient to say that distribution is symmetric?
Wikipedia says in relationship between mean and median:
"If the distribution is symmetric ...
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Existence of the moment generating function and variance
Can a distribution with finite mean and infinite variance have a moment generating function? What about a distribution with finite mean and finite variance but infinite higher moments?
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Proof that moment generating functions uniquely determine probability distributions
Wackerly et al's text states this theorem "Let $m_x(t)$ and $m_y(t)$ denote the moment-generating functions of random variables X and Y, respectively. If both moment-generating functions exist and $...
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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 ...
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Identity of moment-generating functions
Are there any non-identical distributions which happen to have the same moment-generating function?
user9437
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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 ...
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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 ...
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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 ...
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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 $\text{Med}[y]$...
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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 $t$....
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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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Rebuilding a signal based on mean, std, length and more
For some given signals, I have these parameters:
Mean
Standard Deviation
Skewness
Kurtosis
Length (number of samples)
Now I would like to know if I can rebuild the signal (an estimation) based on ...
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How to demonstrate that two samples share the same distribution?
Besides comparing the 1st moment, 2nd moment and 3rd moments, are there any other ways to demonstrate that two samples share the same distribution?
Perhaps use MLE and see if the parameters are ...
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