PDF stands for Probability Density Function (as compared to CDF for Cumulative Distribution Function). The PDF of a variable gives the likelihood for each value of a continuous variable. Use this tag also for PMF (Probability Mass Function) the analog for discrete variables.
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A Probability distribution value exceeding 1 is OK?
On the Wikipedia page about naive bayes classifiers here there is this line "P(height|male) = 1.5789 (A probability distribution over 1 is OK. It is the area under the bell curve that is equal to 1.)" ...
10
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2answers
299 views
Intuitive explanation for density of transformed variable?
Suppose $X$ is a random variable with pdf $f_X(x)$. Then the random variable $Y=X^2$ has the pdf
$f_Y(y)=\left\{\begin{array}{ll}\frac{1}{2\sqrt{y}}\left(f_X(\sqrt{y})+f_X(-\sqrt{y})\right) & y ...
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9answers
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Why does the Cauchy distribution have no mean?
From the distribution density function we could identify a mean (=0) for Cauchy distribution just like the graph below shows. But why do we say Cauchy distribution has no mean?
9
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4answers
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How do you calculate the probability density function of the maximum of a sample of IID uniform random variables?
Given the random variable
$$Y = \max(X_1, X_2, \ldots, X_n)$$
where $X_i$ are IID uniform variables, how do I calculate the PDF of $Y$?
5
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1answer
649 views
Maximum Likelihood Estimation of Inverse Gamma Distribution in R or RPy
I am trying to fit a three parameter inverse gamma distribution to my data in either R or Python. I would like to do this using maximum likelihood estimation (MLE).
The pdf of the three parameter ...
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4answers
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How to get ellipse region from bivariate normal distributed data?
I have data which looks like:
I tried to apply normal distribution (kernel density estimation works better, but I don't need such great precision) on it and it works quite well. Density plot makes ...
3
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3answers
874 views
Closed form formula for distribution function including skewness and kurtosis?
Is there such a formula? Given a set of data for which the mean, variance, skewness and kurtosis is known, or can be measured, is there a single formula which can be used to calculate the probability ...
11
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2answers
737 views
What is the reason that a likelihood function is not a pdf?
What is the reason that a likelihood function is not a pdf (probability density function)?
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Finding the PDF given the CDF
How can I find the PDF (probability density function) of a distribution given the CDF (cumulative distribution function)?
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0answers
81 views
PDF Manipulation for Bayesian analysis
This post pertains to Bayesian pdf manipulation.
Firstly, assuming a prior probability specified as Gamma distribution such that $\alpha = \mu_{0}^{2}/\sigma_{0}^{2}$ and $\beta = ...
11
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1answer
168 views
Deriving Negentropy. Getting stuck
So, this question is somewhat involved but I have painstakingly tried to make it as straight-forward as possible.
Goal: Long story short, there is a derivation of negentropy that does not involve ...
4
votes
1answer
267 views
Estimating PDF of continuous distribution from (few) data points
What are some good, established methods for estimating the probability density function (denoted $f(x)$ from here on) of a continuous distribution, given a sample of points $x_1, \ldots, x_n$ drawn ...
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2answers
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Show that, for $t>1$, $P[\frac{Y}{Z}\leq t]=\frac{t-1}{t+1}$
Let the distribution of $X$ be $U(0,1)$. Let U be the length of the shorter of the intervals $(0,X)$ and $(X,1)$; that is, $Z=min(X,1-X)$ and let $Y=1-Z$ be the length of the larger part. Show that, ...
5
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1answer
219 views
Сonfidence interval of histogram probability density function estimator
There is a circle of radius $R$ and a sequence of points within it. I'm going to estimate a PDF of appearing at elementary area at the distance $D$ from the centre of the circle using a realization of ...
4
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2answers
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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 ...
3
votes
1answer
118 views
PDFs and probability in naive Bayes classification
I have seen a few times the technique of using the Gaussian PDF for continuous features in Naive Bayes. here and here. Illustrated in the first link:
How is this possible? I always learnt that the ...
2
votes
1answer
279 views
Calculating event probabilities in mixed, discrete/continuous distributions
This is a simple question. I am dealing with a "clipped" normal distribution -- say, $N(0,0.5)$ clipped between $[-1,1]$. I would like to calculate the "probability" of a sample, but I know that in ...
1
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1answer
90 views
How to write a function to generate a sequence of points in R?
This is the PDF that I am dealing with:
...
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1answer
142 views
simple sampling method for a Kernel Density Estimator
I have developed a simple Kernel Density Estimator in Java, based on a few dozen points (maybe up to one hundred or so) and a Gaussian kernel function. The implementation gives me the PDF and CDF of ...
