Questions tagged [function]

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

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Integrating functions [closed]

Attached is an integral containing a variable (u) and products of two exponential functions. Kindly assist to proffer solution
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23 views

How to calculate exponential growth when the value is a percentage or probability?

I have a variable x that takes values between 1 and 0 (0<x<1). I want to calculate value of ...
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1answer
45 views

Property of unbiased estimators

If $f(x)$ and $f(y)$ are both unbiased estimators of $\mu$, aka $E[f(x)]$ = $E[f(y)]$ = $\mu$, is it possible that $f((x+y)/2)$ is also an unbiased estimator of $\mu$? We know $f((x+y)/2)$ would be ...
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20 views

statistical model to anlyse each entry with equal weight? and help in r function to do this?

We have conducted an experiment using partial replicated design in 4 replications(blocks). Each block has 84 entries (genotypes) where 12 entries are duplicated (to control environmental variation ...
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1answer
25 views

Function fit to skewed data and non-zero beginning of the function

I would like to find a function that would represent the best fit to represent this type of biological data. More precisely, I would like to estimate expected daily egg production by an insect, based ...
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1answer
29 views

Prove that every linear regression predictor is a linear function

A function $f : \mathbb{R}^D \rightarrow \mathbb{R}$ is linear if both of the following conditions hold. (1) For all $\textbf{x}, \textbf{y} \in\mathbb{R}^D, f(\textbf{x} + \textbf{y}) = f(\textbf{x}) ...
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101 views

How to use statistics to speed up row-wise computations on a data.frame?

I have a data frame with 10,000 rows and 40 columns. I am trying to apply a function to each of these rows. For each row, I am expecting to return a scalar which is the value of the statistic I am ...
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14 views

Polynomials that converges pointwise to a simple function on (-1,1) and bounded by $e^{|x|}$?

I am trying to prove a theorem related to the moment generating function. I will need a sequence of polynomial that converges to a simple function $K_{(-1,1)}(x)$ pointwise on the real line while ...
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19 views

How to weight ranks?

I have a set of responses ranked by my participants. For example, they gave responses A, B, C and ranked them as 3, 2, 1 (or C, B, A). I computed relative frequencies of each responses (A, B, C) and ...
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1answer
24 views

What is the equation of a line fitting a log-log model computed in R?

I am currently stuck, wanting to extract a line function from my fitted line on my log-log model. ...
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17 views

Why does non-parametric approach break down when the joint distribution is estimated by a finite data sample?

I am currently reading the paper on Gradient Boosting Machines - J. H. Friedman, “Greedy function approximation: A gradient boosting machine,” Ann. Stat., vol. 29, no. 5, pp. 1189–1232, 2001, doi: 10....
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Why the output of softmax can be saturated when input differences become extreme? [duplicate]

Like sigmoid function that can be saturated when inputs are extremely different. But how these inputs can cause this function to be saturated?
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sample complexity for class of conjunction of atmost n boolean literals

Why is the no. of functions or $|H|$ taken as $3^n$ while calculating the sample complexity bound and why not $3^{3^n}$ based on the general formula of $k^{k^n}$ where n is the no. of variables in a k-...
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1answer
35 views

replacement error when feeding data from function into matrix in R [closed]

I am trying to write a function that creates simulated datasets. The function takes the argument size, being the size of a group, and it is meant to produce a matrix with 100 columns with values 0 or ...
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25 views

Other functions with sigmoid shape [duplicate]

Apart from the classic logistic or sigmoid function, are there other interesting functions that map real x into a positive space? Maybe they also have an S shape. Maybe inspired by some nature ...
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1answer
63 views

$f$ is a decreasing function whose integral converges. Does $\lim_{x \to \infty}xf(x) = 0$?

My finals are over and I cannot help but ruminate over this particular problem. Could anyone help prove this? Suppose $f$ is a continuous decreasing function on $[0,\infty)$ and $\int_0^\infty f(t)\, ...
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1answer
34 views

How to find parameters of sigmoid function given two thresholds?

Let's say I start with a sigmoid function $$f(x) = \frac{1}{1+\exp{\frac{-(x-c)}{d}}}$$ where the upper limit is 1 and lower limit 0, how can I for example find the appropriate values of the ...
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1answer
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Which type of sums of squares does lm-function in R use?

I ran a two-way ANCOVA in R: ancova = lm(DV ~ IV1*IV2 + CV1 + CV2 + CV3, data = Data) summary.aov(ancova) Anybody know if this uses type III sums of squares? I ...
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1answer
124 views

What is the 'feature function'? [duplicate]

The term 'feature function' is very frequently used in the context of machine learning, but I'm still not sure what it really is. Could anyone give the precise definition? Can it be understood as a ...
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A function depends on a timing

I am writing to ask a question. Recently, I am finding a way to express an outcome as a function of (i) observable factors (ii) unobservable factors (iii) treatment timing. Pretty formally, suppose ...
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Get Continuous Distribution from Discrete Variable: Problem 6.77 of Wackerly, Mendenhall, Schaeffer, 5th Ed

Problem Statement: $\newcommand{\szdp}[1]{\!\left(#1\right)}$ Let $v$ denote the volume of a three-dimensional figure. Let $Y$ denote the number of particles observed in volume $v,$ and assume that $Y$...
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32 views

Calculate probability density by function application

let's assume we have a probability density function which is $$f(X) = \frac{a}{x^a+1}$$ how can we calculate something like this: $$Y = ln(X)$$
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ML approach to learn function as output

I have a question on how to use ML (machine learning) methods for the following task. I have a m-dimensional (field is always over real numbers $R$) input vector $\vec{x}$, and I want to learn the ...
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10 views

Increase weight of a certain outcome in a poisson distribution

I have no background in math, so excuse me if the answer to this is straightforward. I'm trying to build a model that predicts the outcome probabilities of a football game. According to the model, the ...
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1answer
54 views

Is there a name for $\sum P(x) \frac{P(x)}{Q(x)}$ ? (P and Q are pmf)

I know that $\sum P(x) log \left( \frac{P(x)}{Q(x)} \right)$ is the kl-divergence. I'd like to know if there is a name for $\sum P(x) \left( \frac{P(x)}{Q(x)} \right)$ (no log), but couldn't find one. ...
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Relationship between deterministc function of random variables

Given a discrete $P(X,Y,Z)$ let's call $\Omega$ the set of all deterministic functions $f: XYZ \rightarrow W$ and $\Omega'$ the set of all deterministic functions $f': XY \rightarrow V$. Is it correct ...
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1answer
791 views

Problem with user-written function: "Error in shapiro.test(a) : is.numeric(x) is not TRUE" [closed]

Dear StackExchange community, I am trying to write a function to automate some normality-checks. Here is my try (automates Shapiro-Wilk test, histogram and Q-Q plot creation ): ...
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2answers
126 views

How to make the best final prediction of the optimum value in a Bayesian optimization process?

I'm trying to understand the process of Bayesian optimization of a black box function and the bit I'm confused about is how to make the very last prediction of the true maximum after you have made all ...
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1answer
93 views

Fitting model to Wood's lactation curve

I'm trying to determine how I can estimate the following model: $y = at^bexp(ct)$, where $a$, $b$ and $c$ are estimate from a set of data. But I can't figure out how to derive the formula into ...
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Why the definition of a discrepancy or objective fit function does not require monotonicity?

In the context of covariance structure models (as used in SEM), we have $\Sigma$ a population covariance structure, and $\Sigma(\cdot)$, a function of a parameter vector that returns a model-implied ...
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How is an 'ogival function' defined?

Reading on a paper on factor analysis and measurement invariance I find the description of some functions as 'ogival' functions. In Google I find it referenced mostly in papers from the '70s and '80s....
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1answer
63 views

Calclulating and creating x matrix using set.seed function [closed]

I have been asked to evaluate the sum of xi's? what could be wrong with the following code? How to correct it to work? set . seet (1) #set random seed x = rnorm (50) for ( j in 1:50){ s = s + x [ i ] ...
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1answer
27 views

Viterbi Algorithm [closed]

Can someone explain why Is it because for the left argument, we would find the most likely sequence of states given observations and for the right argument, we would eventually find the most likely ...
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22 views

A space of functions and their Fourier Transforms?

Conjugate variables and the Fourier transform are often used to analyze different states of a single object. For example in Quantum Mechanics it can be used to describe changing information about ...
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1answer
63 views

A function of random variables $X_1, ..., X_k$ that goes from $\mathcal{R}^k$ to the reals is measurable with respect to $\sigma(X_1, ..., X_k)$

I'm reading Resnick's "A probability Path" and doing exercise 3 on page 85. The statement is: Suppose $f : \mathcal{R}^k \rightarrow \mathcal{R}$ and $f \in \mathcal{B}(\mathcal{R}^k) / \...
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Do two dependent variables have a functional relationship?

Suppose $X$ and $Y$ are two dependent random variables (e.g. they are the elements of a bivariate normal distribution with $\rho\ne0$). Is it true that there always exists a function $f$ such that $f(...
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Cross entropy and function approximation

My overall question is: the universal approximation theorems can provide a good heuristics on defining the loss function for supervised regression problems, i.e., because universal approximation ...
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22 views

how to solve a complex function

My aim is to solve $$-N (\beta \mu )^{\frac{1}{\beta +1}} s^{-\frac{1}{\beta +1}}-\frac{(\beta +2) N}{2 (\beta +1) s}+t=0$$ The above equation is related to $s$ and the other parameters are constants....
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1answer
199 views

What covariance structure is implemented on the lmer function of R?

I run a Linear Mixed-Effects Models (LMMs) with a repeated measures design with the lmer function on R. ...
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2answers
138 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 ...
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20 views

Relationship between a linear difference equation and the hyperbolic functions [closed]

Considering a linear difference equation \begin{equation} \underbrace{\begin{bmatrix} -p & 1 & 0 & 0 & 0 & \cdots & 0\\ 1 &-p & 1 & 0 & 0 & \cdots & 0\\...
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combining two second order growth functions

I have two second order growth functions of the form Y = (K1 * Yeq^2 * x) / (1 + K1 * Yeq * x) and Z = (K2 * Zeq1^2 * x) / (1 + K2 * Zeq * x), with both Y and Z having an inhibitory effect on each ...
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53 views

how to choose the best fitting function for a data set [closed]

I am trying to find the best fitting function for some data. I have tried with : ...
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1answer
136 views

How do you find the asymptotic distribution of a function of the sample mean?

There are a number of questions on this site that ask for the asymptotic distribution or moments of some function of the sample mean for IID data (see e.g., here, here, here, here and here). All ...
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1answer
158 views

Optimization: Convex function

Problem statement Use the definition of convexity of a function, i.e., that for any $\boldsymbol{x}$, $\boldsymbol{y} \in \mathbb{R}^{d}$ and $\lambda \in \left [0,1 \right ]$ we have \begin{align*} ...
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1answer
297 views

How do you find the minima of a function in python? [closed]

Say we have a quadratic function in x, where the domain of input x is Real Numbers. How can we find the minimum value of the function (output y) in a programming language like python? Immediately ...
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1answer
100 views

Expectation of any function of X, a nonnegative integer valued random variable [duplicate]

How to show that if X is a nonnegative integervalued random variable with distribution F,then $$E(X)=\displaystyle\int_0^\infty \overline{F}(X)dx$$ and $$E(X^n)=\displaystyle\int_0^\infty n*X^{n-1}\...
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62 views

Lapply does not work as expected [closed]

I want to use map or lapply to iterate over a list of dimension variables (dim_list below) using my custom function (transf_fun()). My overall goal is to generate a set of tables and later to pass ...
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1answer
44 views

Expected value of a sum of random variables raised by $e$?

There is a function $y$ defined $$y=\exp(-\boldsymbol{\alpha}'\mathbf{b})\:\:;\:\:\:\:y\in(0,\infty)$$ where $\boldsymbol{\alpha}$ is a vector of random variables and $\mathbf{b}$ is a vector of non-...
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1answer
78 views

Expected value of function with normally distributed input

How can we calculate the expected value of a function $f$ with a normally distributed input? The function can vary. Right now, I am sampling $n$ instances from the normal distribution, calculating $f(...

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