Questions tagged [density-function]

Probability density function (PDF) of a continuous random variable gives the relative probability for each of its possible values. Use this tag for discrete probability mass functions (PMFs) too.

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Calculate the likelihood at the mode of a pdf conditioned on θ [closed]

Assuming that I have the PDF of a random variable X with parameter θ (i.e., f(x|θ)). How is the likelihood at the mode of this PDF computed?
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Estimate at which point a linear model hits a certain value (including probabilities)

I have a simple 1D set of datapoints with a trend, I want to estimate at which point $X_t$ (i.e., at which point in the future) the model will hit a certain threshold $Y_t$: I can fit a trendline to ...
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What is the probability mass function of Rock, Paper, Scissors?

I was curious about the statistics behind the game of rock, paper, scissors. Let's say n people are playing, where n is greater than or equal to 2. If when all n people reveal their play and only 1 ...
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The distribution function of appropriately normalised trimmed mean $T_n(\hat{F}_n)$

A definiton of functional of trimmed mean: $$T^{\alpha}_n = (n-\lfloor \alpha n \rfloor)^{-1} \sum_{\lfloor\alpha n\rfloor + 1}^{n-\lfloor \alpha n \rfloor} X_{(i)}$$ A definition of the optimal ...
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Question on solution of Casella and Berger Exercise 9.10: Showing that $Q(t,\theta)$ is a pivot

My question concerns Exercise 9.10 of Statistical Inference by Casella and Berger: On page 428 the authors say In general, suppose the pdf of a statistic $T$, $f(t|\theta)$, can be expressed in the ...
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How is the q(z) function added at the end of this Bayesian formula?

At the bottom of this Bayesian formula why is a q(z) is brought into numerator and denominator positions? Is this within the rules of Algebra? Could anything be placed in the numerator and denominator?...
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Estimate 2D covariance from 3D matrix where 3rd column contains probability density values

I have an nx3 matrix where the first 2 columns contain uniformly distributed random (x, y) points and the 3rd column contains pdf values evaluated at each point. The pdf values are computed from a ...
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1 vote
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Kernel Density: How do the terms 'global' and 'pilot' translate?

I nearly most of the articles on kernel smoothing or concepts that use kernel density estimations, authors speak of 'pilot' and 'global'. https://link.springer.com/article/10.1023/A:1008925425102 &...
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Expected distance under Gaussian noise

Summary I'm working on a tracking problem, where I'm trying to estimate the position of an object that moves in on plane. In my simulator, at each sampling step I generate a measurement that is given ...
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Random numbers with exponentiated gamma distribution? [closed]

How to get random numbers following "exponentiated gamma distribution"? I tried to search some functions in R and this is what i got: https://rdrr.io/cran/Newdistns/man/expg.html I want to ...
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Why pdf is not considered and cdf is considered for estimating probability of a value [duplicate]

I am a learning statistics on my own and I am a beginner. I came to know that to construct a distribution curve one has to first create histogram. Let's assume that it is a normal distribution. Then ...
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Gaussian closed form solution of marginal likelihood

i have tried some time now to understand a specific step in the derivation of what I think is a marginalization integral. I am still learning about these statistical things and I think I miss ...