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Questions tagged [function]

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

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1answer
11 views

Binary Logistic Regression with the LASSO objective function

I am working on my MSc. Statistic which is on the Penalized Logistic Regression with the LASSO penalty. I am trying to understand the difference in two objective functions: argmin {$\frac{1}{n}$ $\...
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1answer
32 views

Function to fit acid reaction curve

Data in the image below shows a variable DME reacting to the increase in acid concentration. It looks like it has a very fast increase from when the concentration is raised from 0 to 0.5 and then a ...
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0answers
30 views

What is the temperature dependent growth function of phytoplankton for tropical ocean? [on hold]

In tropical ocean, phytoplankton growth decreases with the increase of temperature. In my population dynamics model I want to formulate the phytoplankton growth as a function of temperature for the ...
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40 views

Finding the distribution of a piecewise function of a Gamma random variable

Let random variable $X \sim \text{Gamma}(\alpha,\beta)$. I want to derive the distribution of $Y$, where: $$ Y = \left\{ \begin{array}{ll} a X - k & \quad X \geq \frac{k}{a} \...
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1answer
26 views

Which trigonometric function I should use to generate the temperature with two peaks (i.e.one strong and one moderate peak)?

I want to generate seasonal temperature of Bay of Bengal. I want to do this with a trigonometric function. Seasonal temperature of Bay of Bengal has two peaks. One major peak during April and another ...
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2answers
40 views

How to perform a regression for a multi-function?

How would one perform a regression analysis with a multi-function? That is, where a single X-value can correspond to a number of Y-values? Here is an example: Note that in this example, it is not ...
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1answer
348 views

How to write diff() mathematically?

I am using R/Python diff() operation. e.g., https://docs.scipy.org/doc/numpy-1.14.0/reference/generated/numpy.diff.html I would like to know if there is a ...
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0answers
15 views

How to denote token length in statistics

I have a vocabulary (V) that includes terms. (e.g., V = ['data mining', 'data', 'machine', 'machine learning']) I also have a ...
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1answer
31 views

Expressing as a probability density function [closed]

The measuring error x is a normal random variable. Variance of the error = 4. If distribution of x can be shown by a probability density function f(x), how would you find the analytical expression of ...
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1answer
20 views

How to find emprical PDF by using the normalized histogram?

first of all, thank you for your time, here is my question; Is it possible to find emprical PDF by using normalized histogram? I am trying to learn discrete event simulation and what I see is there ...
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0answers
14 views

Mapping a range of values such that the resulting distribution is uniform [duplicate]

I have a set of values. Let's call the set X with values ... . Those values in [0, 1] have a non uniform distribution (empirically measured). I would like to re-map those values on [0, 1] such that ...
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1answer
38 views

Little problem calculating hazard function

I'm starting to study maths again after a long time without having touch them and I'm currently with survival analysis. I want to get a hazard function h(x), and I know that it can be calculated as ...
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48 views

Formulae for density function replacing probabilistic function

I am working with markov chains and in specific I am working with (Langrock, Roland MacDonald, Iain L. Zucchini, W (2016)). They define a forecast distribution given as: $$ Pr(X_{T+h}=x|X^{(T)}=x^{(...
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17 views

Is Entropy conserved under invertible (but probabilistic) mappings?

I know that under a one-to-one mapping, the entropy is conserved. This was answered very well here: Is entropy conserved under invertible mappings? I am having a doubt about this being applicable to ...
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0answers
115 views

How do I write a random walk with drift ARIMA? [closed]

I modeled oil prices and got the following coeffecients for my arima model with drift. Is this the right way of writing the model?
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1answer
151 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 ...
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1answer
304 views

Difference between function and distribution?

I know this is dumb question, but i am confused to understand it. I have constant function as $$y = exp(-x^2)$$ This also represent gaussian distribution with mean zero and variance of 0.5 Now if ...
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0answers
62 views

Functional Forms of Independent Variables

If our objective is to ascertain the relationship (specifically, sign and significance of Beta coefficient) between independent variables and dependent variable in an OLS regression (cross sectional ...
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3answers
134 views

Does $\mathbb{P}(X < a) = \mathbb{P}(f(X) < f(a))$?

If $f(x)$ is a monotonic increasing function, then does $\mathbb{P}(X < a) = \mathbb{P}(f(X) < f(a))$? My intuition says it's true but I cannot prove the case nor find the name of the theorem.
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0answers
37 views

Is there a function that combines correlation and convolution?

I'm actually trying to find some correlations between functions, and i was wondering if there is a function that quantifies the amount of time we need to shift a curve to have a high correlation with ...
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1answer
539 views

Optimization using the optim function in R with a two parameter exponential distribution

I'm having trouble trying to optimize a two-parameter exponential distribution, by finding the maximum likelihood function and then using the function optim() in R ...
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0answers
27 views

Limiting regression accuracy

I am currently using a LSTM Network to solve a regressional problem. The goal is to predict the payload mass using various time series as input data. For our intents and purposes estimating the mass ...
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0answers
159 views

Mean and std of nonlinear function

I have a gaussian random variable $\xi \sim \mathcal{N} (\mu,\sigma^2)$, and the following function $g(\xi)$: \begin{equation} g(\xi)=-( \xi +\textrm{b}^{\textrm{T}} x) + \left\lVert{\begin{matrix} \...
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0answers
197 views

Problems fitting a model to a variogram

I am having problems fitting a variogram model. I tried to change some parameters to estimate or fix them but I am still not achieving any improvement. I remove trend of the data and use logarithms ...
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1answer
24 views

Can a neural network have an activation function that is a transformation of the parent function?

Neural networks can have activation functions like a tanh(x), a sigmoid function, ReLU, etc.. But can we have an activation function that is a transformation of any of these functions? For instance, ...
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2answers
58 views

Can a neural network learned function $f$ be used for calculating its derivate $f'$?

$y$ is a scalar value, $x$ is an $m \times 1$ vector. Function $f$ is a map $y = f(x)$. Say we have $n$ examples {$(y_1, x_1), (y_2, x_2), \cdots, (y_n, x_n)$}, and we use these examples for fitting ...
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0answers
24 views

User-defined ordered Probit model [closed]

I am trying to build an user-defined ordered Probit model since I will be making changes to the same model at later stage of my research and hence am not using the existing polr function already ...
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2answers
177 views

Function to Produce Periodic Spike and Decay

I am seeking a function (or short algorithm, ideally implemented in R) that produces something similar to the following: See, I would like to be able to generate a vector of $n$ items that follows ...
2
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1answer
35 views

How can I get a sample of a product of two independent random variables?

I have three random variables: $X_1$, $X_2$ and $Y$ such that $X_1$ and $X_2$ are independent and $Y = X_1 \times X_2$. I think that either this question is trivial or I'm making a rookie error, but I'...
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0answers
25 views

Minimize function curve 'length'

Given a set of points $(x_i, y_i)$, how can I find the serie of $ C^\infty $-functions for which the sum passes through all points and for which the length of the resulting curve is minimal; i.e. if ...
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0answers
19 views

Structure coefficients vs. Standardized coefficients in DFA

Could someone give me a clear differentiation between standardized and structure coefficients in Discriminant Function Analysis (aside from standardized being the unique contribution to the function). ...
3
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1answer
36 views

What is f in this Neural Gas neighborhood width formula?

I'm implementing the Online Visualization Neural Gas algorithm, as described in the Estévez, Figueroa 2006 paper. I am having trouble interpreting the formula below (Eq. (4) in the paper): $$\lambda(...
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1answer
20 views

Estimating the mutual information in high dimension when all but one variable are iid

I have a function $f(x_{1},\dots,x_{n})$ where $n$ is large and I would like to estimate the mutual information between the random variable $f(X_{1},\dots,X_{n})$ and the independent and identically ...
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1answer
35 views

Do optimization problems written in argmax form represent a function?

If I write $$\hat{x} = \underset{x}{\text{argmax}}\ f(x,y)$$ can I assume that what is to the right hand side (RHS) of the equal sign is a function in the rigorous sense of the word? Under what ...
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1answer
35 views

How to compare hundreds of one-dimensional functions

I have hundreds (2002 in today's case) of functions of the distance between two objects: $f_1(x)$, $f_2(x)$, ..., $f_{2002}(x)$. They are correlation functions. They all converge to 0 when $x$ is ...
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1answer
58 views

Elements in xlsread output MATLAB version R2018a [closed]

I am trying to understand the function that Matlab executes for importing data from excel file. The very first function in the script generated from import command is the following: %% Import ...
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1answer
116 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 ...
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0answers
20 views

reducing 2 variables of a function into one

I have an experiment where I'm measuring some physical quantity Q as a function of 3 variables which I can physically control (x,y,z). I'm collecting many samples of Q and (x,y,z) and then I can ...
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1answer
39 views

Recovering the Variance when Arbitrary Function is applied to Distribution

Say I have some arbitrary distribution for the value of $a$. I know its mean $\mu_a$ and I know its standard deviation $\sigma_a$. Say I also have some arbitrary relation between $a$ and $b$. I know ...
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1answer
21 views

Generate funciton with specified bases

I am trying to simulate functional data using specified bases and a set of random coefficients. For example, I can generate a function on $[0,1]$ with Fourier basis like $$f(x) = \sum_{i=0}^k a_i sin(...
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1answer
46 views

How to visualise a tiny neural network as a function

Say you have the simplest possible neural network with 1 input, 1 output and 1 hidden variable as depicted below. In this case, the activation function is logistic. I assume between x and y, the ...
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0answers
39 views

Constant/coefficient order and naming in regression functions

This question relates to best practices in Maths and Statistics. When looking at linear regression formulas, they are generally written as $y = a + bx.$ However, in general algebra, the function ...
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1answer
68 views

Two R functions for Bayesian updating with different output

Basically, I have made two posterior (ps) updating R functions; auto1 and auto2. That is, <...
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1answer
908 views

Showing Bayesian updating in R

I'm very new to Bayesian and am very interested in understanding the concept that each posterior from a previous test, can be used as a prior for a current test or in Lindley's (2000) words 'Yesterday'...
1
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1answer
128 views

Proof that joint density is the product of non-negative functions

Let $Y_1$ and $Y_2$ have a joint density $f(y_1, y_2)$ that is positive if and only if $a \leq y_1 \leq b$ and $c \leq y_2 \leq d$, for constants $a$, $b$, $c$, and $d$; and $f(y_1, y_2) = 0$ ...
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0answers
44 views

MLE estimation with no dependent variable in R (likelihood)

I was hoping to estimate two parameters of my model that goes like this: $$Z=\left[(aP_1)^{1-b}+((1-a)P_2)^{1-b}\right]^\frac1{1-b}$$ I have $100$ observations of $P_1$ and $P_2$ in my dataset. Now ...
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0answers
136 views

Approximating a 3d function based on 3d scattered points

Hello I have many 3d points (x, y, z). I have averaged every z with a matching (x, y) value and plotted the resulting means as a surface. The data looks pretty good: The green indicates where the ...
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2answers
4k views

How to model positive S-shaped-function? [closed]

I need to transform my data into a function shown below. My data should fit in the range from 0 to 1. The inflection point should be on 0.5. How I can do this mathematically? Is there any similar ...
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1answer
194 views

Modification of Sigmoid function

I need to model my data into a function like shown in the following picture. But how I can do this mathematically? Is there any similar function to model data that should increase on smaller values ...
2
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1answer
127 views

Estimate monotone function from noisy obsersations

Assume that $y=f(x)$ is an unknown monotonically increasing function of variable $x$. We have access to $N$ observations of this function given as tuples $(x_i,y_i)$, such that $y_i=f(x_i)$. The ...