The mathematical concept of a function. See http://en.wikipedia.org/wiki/Function_(mathematics)

learn more… | top users | synonyms

0
votes
0answers
20 views

Cumulative Function Values [on hold]

I'll have an exam next Thursday, I'm studying for the exam but I got a doubt in one exercise. Thats it: Given this values: 2.5, 3.6, 5.7, 8.3 and 1.0 determine if or not the values follow this ...
3
votes
2answers
116 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 ...
0
votes
0answers
15 views

Help in identifying this nonlinear system

In the paper: http://inds08.uni-klu.ac.at/INDS2008/INDS08_System_Identification_using_Symbolic_Chaotic_Sequence.pdf there is a chaotic map in Eq(11) $$c_{n+1} = \frac{\gamma c_n(1-c_n^2)}{1+\rho ...
0
votes
0answers
14 views

A Binary Classification to Distinguish two Different Models?

I have two functions, a step function $f(x)$ and an inverse exponential function $g(x)$. Together, they explain virtually all the data when combined as a piecewise function. Some of the data points ...
0
votes
1answer
62 views

Estimate variance of a function given variances of variables

I'm given the mean and the standard deviation of N random variables $A$, $B$, $C$, $D$... I compute the function $f:=f(A, B, C, D...) = \frac { AB... }{ CD... } $. How can I estimate the variance of ...
4
votes
1answer
118 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 ...
0
votes
0answers
15 views

Periodic radial-basis

I'm trying to implement a radial basis fuction using guassian pdf as basis, the problem is I'm working on a spherical coordinate system; in other words I'm representing the surface of a sphere as a ...
-2
votes
1answer
61 views

Decomposing a random variable with random mean into a sum

I have two random variables: $X\sim \mathcal{N}(0,\sigma^2+1)$. $Z$, a gaussian with mean $X$, distributed so that $E_{X,Z}[(X-Z)^2]=s^2.$ We know that: $$s^2\geq\sigma^2+1 \Leftrightarrow Z ...
1
vote
0answers
28 views

Algorithm to identify a correct input for only one number [closed]

Hello I'm hoping that you good folks here at CrossValidated can help me with this. I'm looking for an algorithm that takes an integer as an input and returns two types of values. One type of value ...
0
votes
0answers
34 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
21 views

Learning a spatial function

I have some observations of a variable y, that varies spatially. For each observation, I also have a lat, long tuple. I have some 50 or so observations. Besides conducting some exploratory analysis ...
0
votes
2answers
106 views

Apply function generating random numbers to a matrix (R) [closed]

I have a function which basically creates a random number. Now I want to apply the function to a matrix for given conditions to replace the value in the matrix with the random number created by the ...
0
votes
0answers
60 views

What function best describes this plot?

The X and Y have values only between 0 and 1.
1
vote
1answer
54 views

Find distribution of underlying feature

Let's say I have a dataset with values for the variable $W$. The distribution of $W$ doesn't follow any obvious known distribution. I have a model that gives $W$ as a functions of $E$ and $K, W = ...
2
votes
0answers
43 views

Using A Time Series To “Scale” Another

I know the "average theoretical cost per impression" for Jan 13 - Dec 13. I have other monthly time series for "total # of impressions", "total # of clicks" and "total number of conversions" for Jan ...
0
votes
0answers
35 views

Calculate pdf of complex model

I'm trying to model the distribution of effects of mutations (let's call it s) in evolution but I'm stuck in generating the probability distribution function (pdf) for my model. So, my model is a ...
0
votes
1answer
55 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 ) = ...
0
votes
0answers
30 views

Validating sameness or difference of a relationship

I am measuring a response variable Y(x,t) which theoretically is a function of both time (t) and space (x). I have measurements for Y as t varies for different spatial points x. On inspecting visually ...
2
votes
1answer
84 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 ...
0
votes
0answers
13 views

Tendency tags based on series of numbers

I am trying to create tendency tags based on historic data. Ie, I have the following series always ordered in time: [w,x,y,z] where: ...
1
vote
2answers
52 views

Can you compare probabilities of an epidemic by knowing R0 values?

In comparing two diseases with different basic reproduction numbers (R0), is it possible to use the R0 values to calculate the probability of an epidemic spread through a population? For example, if ...
0
votes
0answers
65 views

Why SVM with RBF is similar to KNN with prototypes search?

I explored similar questions and everything I can see is that both kNN and RBF are non-parametric methods to estimate the density of probability of your data. However, I am not sure if this has ...
2
votes
2answers
99 views

What is this formula?

i have been asked to plot a graph of the residuals from the following formula: |y(hat)/y|-1 they said that it was MAPE but i have the formula for MAPE as: ...
1
vote
0answers
23 views

How can you cluster a set of functions with unknown functional forms?

Say you've $N$ functions $f_N(x)$ defined on a regular grid $x$. You don't know the form of $f(x)$, you've only got several realizations of it. The different functions are related to each other ...
0
votes
1answer
56 views

Correct notation wrt. uniform distribution

Assume that I have a discrete set $L$ and a transformation $\phi: L \rightarrow [0,1]$ that normalizes set $L$ such that now values belonging $L$ are uniformly distributed among the unit interval. ...
1
vote
1answer
96 views

Generating functional-form PDF from Max Likelihood Estimation

For the purpose of this question, please consider me a stats newbie. I'm working on a (very fun!) research project which involves estimating a pdf of "personal values" -- i.e. how much a certain ...
2
votes
1answer
63 views

Given the distribution of a variable X, what is the distribution of f(X)?

Suppose I know the mean and standard deviation of a (roughly) normally distributed variable x. Is there any way for me to calculate the mean and standard deviation of f(x)? The particular problem I ...
0
votes
1answer
113 views

dealing with exponentials in python - infinities and overflows [duplicate]

In a machine learning algorithm that I'm using, I need to get the exponential values of something in one of the steps. This is the step that I'm dealing with right now: I've already got all the ...
1
vote
0answers
31 views

Is $Max${$F(X),G(Y)$} necessarily a distribution function?

If $F(X)$ and $G(Y)$ denote two distribution functions, then is $Max${$F(X),G(Y)$} necessarily a distribution function as well?
0
votes
0answers
48 views

How to interpret basis function that yields vector in machine learning algorithm?

I'm struggling to understand what $\phi(x_{N+1})$ is in this excerpt of an algorithm (namely Linear Bayesian Regression embedded in other algorithm): $c_i = \gamma_i / \sum^L_{j} \gamma_j$ ...
8
votes
2answers
202 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 ...
1
vote
2answers
729 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 numbers. It is data extracted roughly every minute from a machine ...
0
votes
2answers
58 views

cumulative distribution function , cdf problem

I cannot understand how step 2 transformed to step 3, anybody help me please ???
2
votes
1answer
229 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
57 views

Gradient without function, just testing and training data

I am new to optimization in particular so I think what I am looking for is vocabulary to describe a particular area of problems. In many (all?) optimization algorithms you need to take the gradient of ...
1
vote
1answer
540 views

Function to find the quantile in a vector corresponding to constant $x$ [closed]

Suppose I have constant x=0.1 in the language R and I have a vector vec = rnorm(200). Is ...
7
votes
2answers
248 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 ...
2
votes
1answer
370 views

R - Calculate trendline and extend it for 365 days automatically

I have daily data with logarithmic decreasing trend (around 30-days-data). In excel I'm calculating these data's trendline and with that trendline equation, I'm projecting these values to 365-days ...
2
votes
1answer
43 views

Requirements for evaluation function in evolutionary algorithms

For a publication I'm looking for references for generic requirements of evaluation/fitness functions in evolutionary (more specifically genetic) algorithms. I could come up with some requirements ...
0
votes
1answer
97 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 ...
1
vote
1answer
392 views

Finding the similarity between two functions

I am a first-year grad student in Computer Science, and I need some help with a problem that I think is statistically oriented. I have taken a statistics course, but it was abysmal and I haven't had ...
1
vote
1answer
127 views

Cumulative function to probability density function

I have some data points for which I would like to show the density using Python, but the package SciPy is not working for Python 3.3. I am looking for a solution to be able to plot some data in the ...
3
votes
1answer
380 views

R: Defining a new continuous distribution function to use with Kolmogorov-Smirnov Test

I wish to run the Kolmogorov-Smirnov test on my data to determine how well it conforms to a specific continuous distribution function I have in mind. If my understanding is correct, the ...
1
vote
1answer
755 views

calculation of correlation time?

I have two time series of a two realizations of a random process, the process fluctuate around an average so i consider that is a ergodic process. I compute the time correlation function, but i need ...
0
votes
1answer
98 views

Can I represent a non-boolean function with a TREE?

I have a question in respect to tree representation of a non-Boolean function. Is there any problem in representing a function from space Boolean->Limited Integer or Limited Integer->Limited ...
1
vote
0answers
83 views

Question related to binomial distribution

Let $X \sim Binomial (n, p)$ with both $n$ and $p$ known. Suppose for some non-increasing function $G:[0,1] \rightarrow [0,1]$, and some fixed $c_0 \in [0,1]$, we have that \begin{align} ...
9
votes
2answers
390 views

How to estimate the accuracy of an integral?

An extremely common situation in computer graphics is that the colour of some pixel is equal to the integral of some real-valued function. Often the function is too complicated to solve analytically, ...
6
votes
1answer
827 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 ...
3
votes
1answer
181 views

Objective function in linked prediction models

I would like to use R “optimize” function to estimate the model: $\hat{Y_{t}}=a\cdot \hat{Y}_{t-1}+b\cdot X_{t}+c\cdot X_{t-1}$ Important thing is that the predition $\hat{Y_{t}}$ (let’s say ...
0
votes
0answers
160 views

Posterior mean of exponential functions: how to do it with MCMC?

I am struggling with estimation of posterior mean of simple exponential function f(x)=exp(x). Mixing of the chain is quite good and there is no problem with estimation of simple mean, but since ...