Questions tagged [function]

A mapping between a set of inputs and a set of outputs.

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15
votes
3answers
50k views

How to find the mode of a probability density function?

Inspired by my other question, I would like to ask how does one find the mode of a probability density function (PDF) of a function $f(x)$? Is there any "cook-book" procedure for this? Apparently, ...
12
votes
1answer
5k views

Proof that if higher moment exists then lower moment also exists

The $r$-th moment of a random variable $X$ is finite if $$ \mathbb E(|X^r|)< \infty $$ I am trying to show that for any positive integer $s<r$, then the $s$-th moment $\mathbb E[|X^s|]$ is ...
8
votes
2answers
294 views

How to properly handle Infs in a statistical function?

Suppose I have a function such like: f <- function(x){ exp(x) / (1 + exp(x)) } it's supposed to work for any real value of x, but actually it returns NaN ...
5
votes
2answers
105 views

Generating uniform points inside an $m$-dimensional ball [duplicate]

The present question follows on from some other questions on this site asking how to generate uniform points inside a disc (see e.g., here, here and here). The natural extension of that problem is to ...
12
votes
3answers
3k views

Can a neural network learn a functional, and its functional derivative?

I understand that neural networks (NNs) can be considered universal approximators to both functions and their derivatives, under certain assumptions (on both the network and the function to ...
8
votes
1answer
2k views

How to understand the geometric intuition of the inner workings of neural networks?

I've been studying the theory behind ANNs lately and I wanted to understand the 'magic' behind their capability of non-linear multi-class classification. This led me to this website which does a good ...
1
vote
3answers
3k views

Difficulty with auto.arima function results

I am new to R and the ARIMA model and I am attemping to forecast 1440 values into the future using a base of roughly 5000 ...
10
votes
3answers
209 views

Is there a way to recover a temporal dependence structure in a time series from a regression against time?

Consider a time series: $X_1,X_2,...X_{n-1},X_n$ This series can also be written as a function of time $X(t)$, so that: $X_1,X_2,...X_{n-1},X_n = X(t_1),X(t_2),...X(t_{n-1}),X(t_n)$ Most ...
6
votes
2answers
7k views

How to measure the shift between two cumulative distribution functions (CDFs)?

How to measure the shift between two cumulative distribution functions (CDFs)? Specifically, in the image below, how meaningful is the shaded area? It is supposed to measure the shift between the ...
10
votes
1answer
411 views

Proving a sequence decreases (supported by plotting a large number of pts)

Many of the questions I've posted on SE in the last month have been in the goal of helping me solve this particular problem. The questions have all been answered, but I still can't come up with a ...
8
votes
2answers
399 views

Function of random variables

I am not sure what the right keywords would be for this but I would like to know if it is possible to apply functions to random variables. I think it may make sense in terms of expected value but I ...
1
vote
1answer
2k views

ReLu vs a linear activation function

I read this great answer about how ReLu could approximate non-linear functions. However, if ReLu can approximate such functions, why cant linear activation function do the same? If they can, why ...
3
votes
1answer
231 views

Time Series Function - Constant vs Piecewise

I have daily data for online marketing $ spend and the number of clicks to the website gained. I want to determine a function that 'maps' the two together. I cannot use normal linear regression ...
2
votes
1answer
2k views

Calculating power function for ANOVA

There are several functions in R to calculate the power of a test, for example, the pwr-functions of the pwr package. My question is how we get this function for ...
0
votes
1answer
165 views

Can I derive the PDF ( f(C) ) from a spatial function defined as C(x)?

Say I have a random variable (such as concentration) that is defined spatially by some function $C(x)$. I would like to derive a PDF $(f(C))$ from the concentration function $C(x)$ over some domain ...
4
votes
1answer
472 views

Arbitrary function approximation in one dimension

Suppose we have some arbitrary function $f: X \mapsto Y, X \in \mathbb{R}, Y \in [0, 1]$. It may be smooth but it may not. I am looking for some way to approximate this function given samples drawn ...
3
votes
1answer
2k views

How to calculate the probability of an event occuring within n days, if we know the probability of it occuring per day

If an event can occur at most once per day, and the probability of it occurring is 10%. What is the upper-bound on the probability that the event occurs in an interval of L days of a month (assuming ...
1
vote
1answer
646 views

Implication of Hazard Rate?

So from my understanding, the hazard rate is not a probability but a rate of an event happening at any one period of time. Can someone please tell me the implications of a hazard rate value. Would ...
0
votes
1answer
228 views

What is the name of the resulting function?

Consider the following population regression model: $$y_{i} = \beta _{1} + \beta_{2}x_{i} + \epsilon _{i},$$ where $i=1,...,n$. Assume $\epsilon \sim iid$, with the pdf in equation: $f(\epsilon ) = \...
-2
votes
3answers
517 views

Find a mapping of two probability mass function to another probability mass function

Lets' $p$ and $q$ are probability mass functions of two discrete random variables. I need examples of functions $F(p,q)$ that $r = F(p,q)$ and $r$ is a probability mass function for some random ...