Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [piecewise-pdf]

A piecewise pdf is a probability density function that is defined on a sequence of intervals, within each of which, a separate function describing the behavior of the pdf over the interval is defined.

A piecewise PDF is a probability density function that is defined on a sequence of intervals, within each of which, a separate function describing the behavior of the PDF over the interval is defined.

References

http://mathworld.wolfram.com/PiecewiseFunction.html

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Acceptance/rejection sampling and inverting CDF (R code illustration included)

I have the following example: Acceptance/rejection sampling In some cases the cumulative distribution function might not be (easily) invertible. For example if $X$ has the probability density function: $$f_X(x) = \begin{cases}…
The Pointer
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Sampling from a piecewise linear probability density function

I have a pdf modelled as a piecewise linear function that I can represent as the sequence of pairs of real numbers standing for the points in the of the piecewise line: $\{(x_{1}, y_{1}), \dots, (x_{n}, y_{n})\}$ such that each $x_{i}, x_{i+1},…
rano
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How to understand this probability density function with continuous random variable

Could anyone help me? I don't want the solution. Instead I'm just looking to understand what this means: x 2 Is this the Binomial Coefficient? How is this related with PDF?
Overflow012
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What are reasonable ways to plot the "pdf" of a censored random variable?

Objective: Just to help close a hole in my statistical knowledge (as opposed to having a practical subject matter need), I want to know what are some of the ways to display what I am calling a probability density function when the probability…
JimB
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How to generate samples from a distribution with jump points?

I'm trying to simulate a survival dataset, with the censoring variable $X$ following a continuous distribution with mass points. The distribution is $$f(x) = \begin{cases} \lambda_1e^{-\lambda_1x}, & 0 \le x \leq a \\ \lambda_2e^{-\lambda_2x}, & a <…
Yujian
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Inverse transform method with piecewise pdf

I am having trouble using the inverse transform method with the generalized inverse $$F^{-1}(u) = \inf \{x : F(x) \geq u\}$$ In this case, I have a piecewise pdf $$f(x) = \begin{cases}x, & 0 \leq x \leq 1 \\ 2 - x, & 1 < x \leq 2 \end{cases}$$ which…
The Bosco
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Distribution of a dice pool

The article Three Basic Distributions from AnyDice shows the distributions (and cumulative distributions) of 1d10, 2d10 and 3d10. Looking at the graphs, it seems there is a pattern here: 1d10: the distribution is a piecewise polynomial with 1 piece…
CidTori
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Posterior distribution from piecewise likelihood

Consider a hierarchical Bayesian model for analysing data from an inhomogeneous Poisson process that we observe in discrete time. Let $Y_i, i = 1,...,n$, be the number of events occurring in the time interval $[i−1,i]$ and assume that $P(Y_i=y_i |…
Grautus
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How do I calculate significance with piecewise models?

I am running a piecewise logistic model to generate the survival curves of students not dropping out of school. The model-based probabilities are something like $$ p_1=P(\texttt{dropping out at }t=1) \\ p_2=P(\texttt{dropping out at }t=2)…
Martha Moreno
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Inverse CDF (Quantile) of Piecewise Function

This question may be insanely simple, but I'm unsure. Let's say we have the following function: $$ f(x) = \begin{cases} x & 0 \leq x < 1 \\ x-1 & 1 \leq x < 2 \\ 0 & \text{otherwise} \end{cases}$$ The CDF is obviously $$ F(x) = \begin{cases}…
TheAkashain
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Formalism to cope with probability density functions defined piecewise (in the second dimension)

I'm not sure how to pose this question, as I lack the correct terminology. Actually, my question tries to obtain insight on the terminology and notation to cope with the following problem: I have a probability density function that depends on two…
Pythonist
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Expected value with piecewise probability density function (PDF)

I am continuing the prepare for an exam by reviewing handouts from an old statistics course I took. The handout came with a set of solutions prepared by the instructor, but I suspect that one of the answers is wrong. If the answer the instructor…
StatsStudent
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