# Questions tagged [function]

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

206 questions
Filter by
Sorted by
Tagged with
16 views

### Integrating functions [closed]

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

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 ...
31 views

### 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 ...
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 ...
8 views

### 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 ...
23 views

### Get Continuous Distribution from Discrete Variable: Problem 6.77 of Wackerly, Mendenhall, Schaeffer, 5th Ed

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

### 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 ...
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 ...
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. ...
27 views

### 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 ...
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 ): ...
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 ...
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 ...
14 views

### 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 ...
27 views

### 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....
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 ] ...
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 ...
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 ...
63 views

55 views

### 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 ...
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....
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. ...
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 ...
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\\...
32 views

### 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 ...
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 : ...
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 ...
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*} ...
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 ...
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 $$E(X^n)=\displaystyle\int_0^\infty n*X^{n-1}\... 0answers 62 views ### Lapply does not work as expected [closed] I want to use map or lapply to iterate over a list of dimension variables (dim_list below) using my custom function (transf_fun()). My overall goal is to generate a set of tables and later to pass ... 1answer 44 views ### Expected value of a sum of random variables raised by e? There is a function y defined$$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-...
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(...