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

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8 views

True or false? “sum of an m-strongly convex and a convex function is m-strongly convex” [migrated]

I would like to know if the following conjecture is true or false? If $f(x) = g(x) + h(x)$ where $g$ is m-strongly convex and $h$ is convex, then $f$ is m-strongly convex. NOTE: For a ...
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0answers
12 views

How to estimate parameters of distrubution function where CDF data is known but no sample dataset [closed]

I would be very appreciated if someone help me. I have F(x) (Cumulative density) values for specific x values which is not equal interval but I have not any sample data to estimate parameters of ...
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0answers
16 views

RDD - function property

Is the fact the RDD draws a function that is not bijective (perhaps I am being incorrect on this point? actually there is always one x->y and a discontinuity of the function at the cut-off) related to ...
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1answer
47 views

log hazard function in R

I'm trying to write out the log hazard function of the lognormal distribution and use this in R. Using the survival function: and the hazard function: I have the following for the log(hazard): ...
4
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1answer
60 views

Converting log hazard function to survival probability

I am currently working through a survival problem and I wanted to get some advice with how to proceed. I wanted to estimate survival probabilities over time based on knowing only the $\log({\rm ...
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1answer
46 views

How to extract distribution of r.v. $X$ from probability generating function of $X$?

How to extract distribution of r.v. $X$ from probability generating function of $X$? The p.g.f. of $X$ is: $$G_X(t)=\sum_{k=1}^{\infty}t^kP_X(k).$$ That is, if $G_X(t)$ is known, then (how) can one ...
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0answers
18 views

Minimizer of a function containing response and predicting variables

Can anyone please give me the expression of the "minimizer" of $$\sum_{i = 1}^n \vert y_i - b x_i \vert + \sum_{i = 1}^n (y_i - b x_i)^2 \quad \quad ?$$ I am unable to find this expression on the ...
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0answers
15 views

Terminology for a 1-d summary of a high-dimensional space?

Overly pedantic question ahead. Suppose I have a huge matrix M that has a row for everyone who was at Disneyland on some particular date, a column for the person's ...
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0answers
19 views

What does this evaluation function mean?

I am solving a prediction problem where I am supposed to predict the number of clicks, given some historical Data. I am told that my predictions will be evaluated by a normalized weighted mean square ...
0
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1answer
293 views

Could not find function in R? [closed]

I am getting the error: Error: could not find function "rlm" where rlm Why isn't R working for certain functions? I wrote fit<-rlm(z~cbind(time(z),time(z)^2)) Error: could not find function ...
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3answers
141 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, ...
3
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1answer
65 views

Let $X$ be a random variable and $f$ an invertible function. Then the CDF of a random variable $Y=f(X)$ always exists?

Let $X$ be a random variable and $f$ and invertible function. The cumulative distribution (CDF) of $X$ is defined as $$F_{X}(x) = \mathrm{P}(X\leq x).$$ The CDF of $Y=f(X)$ is then $$F_{Y}(y) = ...
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0answers
40 views

NLME loop over big dataset and multiple phenotypes

I am running a linear mixed effects model (nlme) and I would like to run the model over 1000 columns (x: independent variable e.g. x1…x1000) and I would also like to run this for a number of depended ...
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0answers
12 views

Naming of a Function which Estimates Other

Sometimes we can’t optimize a function (or objective) itself (e.g. because of complexity), and thus we try to optimize another function (or objective) that is similar to it. I think there was a name ...
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0answers
33 views

Expected value of bounded function?

The expected value of a function is $$E[g(x)] = \int_{-\infty}^{\infty}g(x)f(x)dx.$$ What happens if $g$ is a function such as $g:\mathbb{R}\rightarrow]a,b[$? Does the expected value exist? Should ...
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1answer
55 views

Existence of expected value of function

According to Wikipedia, the expected value of a continuous random variable is $$E[X] = \int_{-\infty}^{\infty} xf(x) \mathrm{d}x.$$ Suppose $f$ is a function such as $f:\mathbb{R}\rightarrow ...
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42 views

Confidence interval for GLM or the maximum of a function?

Imagine I have a set of (xi,yi) measures. I can show it on a scatter plot I want to choose the value of x that maximizes y, or I could fit a function and find the values of the parameters that ...
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1answer
92 views

How to calculate the probability distribution F(X,Y) when the distributions of X and Y are known?

Suppose $X$ and $Y$ are normally distributed with known means and standard deviations. How do I calculate what is the probability distribution some function $f(X,Y)$? For example, say $f(X,Y)=2X+Y$. ...
0
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1answer
153 views

How to find (using R) the function which my experimental data follow?

I have an experimental time-depending data (Mean as a function of Time). I want to find the function which my data follow. I have already tried fitdistr and Gam, but it hasn't really helped. Could ...
3
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2answers
160 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 ...
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0answers
16 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
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1answer
71 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
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1answer
165 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 ...
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18 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 ...
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1answer
103 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 ...
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0answers
46 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 ...
1
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1answer
75 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
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1answer
23 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
318 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 ...
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0answers
62 views

What function best describes this plot?

The X and Y have values only between 0 and 1.
1
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1answer
58 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 = ...
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52 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 ...
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44 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
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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 ) = ...
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0answers
39 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
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1answer
90 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 ...
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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
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2answers
66 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 ...
2
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2answers
160 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: ...
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0answers
26 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 ...
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1answer
66 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. ...
2
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2answers
125 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
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1answer
82 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
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1answer
187 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
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0answers
34 views

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

If $F(X)$ and $G(Y)$ denote two distribution functions, then is $Max${$F(X),G(Y)$} necessarily a distribution function as well?
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50 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): $c_i = \gamma_i / \sum^L_{j} \gamma_j$ ...
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2answers
212 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
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3answers
1k 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
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2answers
61 views

cumulative distribution function , cdf problem

I cannot understand how step 2 transformed to step 3, anybody help me please ???
2
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1answer
293 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 ...