# Questions tagged [function]

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

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### 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, ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
I have daily data for online marketing $spend and the number of clicks to the website gained. I want to determine a function that 'maps' the two together. I cannot use normal linear regression ... 1answer 2k views ### Calculating power function for ANOVA There are several functions in R to calculate the power of a test, for example, the pwr-functions of the pwr package. My question is how we get this function for ... 1answer 165 views ### Can I derive the PDF ( f(C) ) from a spatial function defined as C(x)? Say I have a random variable (such as concentration) that is defined spatially by some function$C(x)$. I would like to derive a PDF$(f(C))$from the concentration function$C(x)$over some domain ... 1answer 472 views ### Arbitrary function approximation in one dimension Suppose we have some arbitrary function$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 ... 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 ... 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 ... 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 ) = \...
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 ...