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Questions tagged [fitting]

The process of fiting some statistical model to a particular set of data. Mostly done on a computer, and using varied numerical methods such as optimization or numerical integration, or simulation.

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How to fit a Beta-Binomial Distribution to a dataset [duplicate]

I have a data set which is defined over positive integers and I have reasons to believe it follows a beta-binomial distribution. I am aware there is the ...
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Is there a difference in finding p-value using likelihood ratio vs minimum deviance statistic?

I am trying to fit my data to a distribution and find the fit parameters and associated p-value. If I use the -2-log likelihood ratio, or G-test, vs the minimum deviance method, will I get different p-...
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How to choose some discrete probability distribution to fit a target discrete probability distribution? [closed]

I have a set of vectors, each of which represents a discrete probability distribution, now I want to use some of them to simulate a certain discrete probability distribution. For instance, the ...
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1answer
33 views

Should I subtract lower bound from Gamma distributed data before estimating distribution parameters?

I have some real world data that reflects waiting time in a system. As it's about waiting times I assume it's Gamma distributed and visual check (histogram overlaid by a fitted Gamma PDF) shows no ...
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1answer
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What model/significance test should I use to see if there's any significance between male and female sexual dimorphism on temperature over time?

In my lab I need to test if there's an significance between male and female sexual dimorphism on body temperature over 40 minutes. The temperature is simulated with a heat lamp and is turned on at 0 ...
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1answer
27 views

How to calculate “start” value for fitdist function for a Tracy-Widom distribution?

I have a data with 100 million data points, and I'm trying to make a Tracy-Widom distribution fit to this data using the following R script: ...
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k-fold cross validation: What is the proper reward when fitting a distribution's hyperparameter? And how to combine across folds?

There is a hyper-parameter $h$ of a distribution $D_h(z)$ I am trying to fit (think like the bandwidth in KDE). The probabilistic story is as follows: $z$ comes from the distribution $D_h$, and then $...
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Understanding the Cullen and Frey plot

I would like to figure out which distribution fits my data best. Here is the histogram of my data : I used the fitdistrplus package in R to try to find the best ...
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Model/predict the number of malaria-infected cells

Background: In order to determine the severity of a Malaria infection, one takes a sample of red blood cells and determines, through a microscope, the number of cells infect by the malaria parasite. ...
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13 views

Dynamic transformations on an inferred time-scale [duplicate]

Sorry if this is a duplicate, I have limited knowledge on data science, so I don't know the correct terms to look for and don't know if there's already an answer out there. I have two datasets which ...
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9 views

How to model the fitness of one individual regarding a dynamic sample?

Briefly introducing the project, I'm currently working on a similarity optimization problem, minimizing the distance between 2 curves, obtained through my objective function. The optimization ...
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Fitting distributions using the dispersion of Z-scores

I work for a medical testing company and I've inherited some legacy code written by someone who has since left. I understand the reasoning behind most of what is there, but the final step is something ...
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Best tools to fit simulation data to observation. Tuning parameters

First off, sorry I am a bit of a noob to the data science world. Looking for help on the following, thanks in advance. My problem is as follows: I have observation data from a complex experiment, ...
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Fitting a model in R [closed]

How do I fit a model of the form $y = a + b \exp(−cx)$ to my data in R?
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100 views

fitting non-normal multivariate distributions in R

I have many (n=317,823) observations on two variables. I want to fit a bivariate distribution to my observations, in order to identify descriptive features of the distribution (quantiles). However, my ...
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Significance of difference in quality of fit between two sets of parameters of the same model

I have one experimental data set and two fits to it. Both fits were generated from the same model - the fits are different because the parameters of the model are different. The fit from set 1 is ...
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27 views

Working out a metric for the goodness of fit for 2D data in time

I have a dataset which I wish to optimise a fit for. The data might look something like I.e. orange is t=0, blue is t=1, and green is t=2. I wish to find a fit. I have a differential equation ...
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Model that fits ellipse for pupil detection

I have an eye tracking system which fails to correctly detect the pupil in the camera image when there is a larger luminance gradient across it. This happens if the pupil is very dilated. For me it's ...
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2answers
108 views

Male-female height difference estimation from thresholds

Introduction. Assume that two populations $A$ and $B$ are distributed with normal distributions $N(\mu_A, \sigma_A^2)$ and $N(\mu_B, \sigma_B^2)$. This is a general problem, but as an example, I will ...
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1answer
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Fitting a multivariate Gaussian with extremely sparse samples

We have a multi-variate Gaussian distribution. For instance with 3 variables. The correlations between the variables are important! We are fitting it to data, however, the samples are such that each ...
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22 views

Should the reduced chi-sq of a fit to some points be the same as the reduced chi-sq of a fit through a weighted average of those points?

I have nine data points with three of them taken at x = 2, three taken at x = 4, and three more taken at x = 6. I came up with a straight-line fit for these points, and found the reduced chi-sq of ...
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Finding expected range of values in multi variable reduction

For a least-squares reduction to find expected values for $a,b,c,d, ...$ from a number of equations like: $a + b = n_1$ $a + c = n_2$ $b + d = n_3$ $c + d = n_4$ ... My question relates to ...
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1answer
116 views

How to improve this time series model?

I am trying to fit a time series model for household data which is a time series variable. Initially my data looks like this, Since the data does not seem to be stationary I differenced the data. ...
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Distribution identification with respect to number of fitting parameters

I want to check a sample of measurements against different distributions in order to determine the underlying distribution. Distributions should be yielded based on probability or goodness-of-fit ...
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59 views

Is it possible to fit a binomial cumulative distribution with only three data points in R?

I have three data points (0,0), (30,0.1538), (60,0.4914). Is it possible to fit a binomial cumulative distribution function only using these three points in R? If not, what sort of extra information ...
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1answer
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Determining error between two surfaces given same discrete inputs?

Apologies if this isnt the best SE forum to ask on, but it seems relevant here. I have, as an output of a machine learning algorithm, a surface in z, which has known increments along x and y. These ...
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27 views

Uncertainty from equation involving fitted parameters [closed]

I want to estimate the uncertainty of a calculation which involves a quantity from a fitted mathematical model. More specifically, the end calculation would be something like: P = x / A_tot where I ...
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1answer
100 views

Fitting the Poisson distribution to binary data

I'm studying several time series. The variables of interests are dummy variables which take value 1 when a certain event happened, 0 otherwise. I want to find the best distribution to describe these ...
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25 views

Inestability of BIC when selecting nested models

Currently I am working with spline regression and a method for selecting knots adaptively. My method gives me a set of potential knots that generally has a large number of elements. Following He et al....
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32 views

R - Fitting a Coxian phase-type distribution to data

Using R, I would like to fit a Coxian phase-type distribution to a vector of waiting times ($t_i$) where the $\mu$'s and $\lambda$'s are unknown i.e. I want to find ...
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10 views

Fitting of 2D data [duplicate]

I have a 2D data-set. If we plot, it looks like above. Now if I want to know the central value of the distribution $\theta$ and width of the distribution $W$. How do I do that?
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When making a fit to data without weights, how reliable are the fit errors?

I often need to fit data which is a spectrum. And it isn't possible to have many identical spectrum from which to produce error bars on the individual points in an averaged spectrum. So my question ...
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83 views

Change variable to log transformed or keep original?

A log transformation of the dependent variable is sometimes recommended as a remedy for some cases of non-normal distribution of residuals after fitting a linear regression model. What is the proper ...
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34 views

Do mismatches in areas of peak density affect the KS-test more than mismatches in low-density areas?

In the following plot you see my empirical data (black) plotted against a hypothesised distribution (blue). However, a KS-test shows that there is no indication that my sample follows this ...
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Plot confidence interval of average polynomial fit from coefficients

I am studying the propagation of a wave and to do that I want to follow the position of my maxima over time. In order to do that I thought to fit a polynomial on the data of each replicate, then save ...
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1answer
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Are $h_i(x)=x^{-\alpha_i}$ okay basis functions for fitting?

I have some pairs of data ${(x_1,y_1),..., (x_n,y_n)}$ genereated by some process and would like to fit it with a function so that $y_i \approx \hat{f}(x_i)$. By plotting the $(X,Y)$ on a 2D plot, ...
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1answer
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Based on the ideas of Parameter Estimation and Fitting Probability Distributions, what stops us from making any function be a PDF(PMF)?

Currently I am doing an introduction to parameter estimation and fitting probability distributions to sets of data. So in a small synopsis what I understand the whole process to be like is the ...
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421 views

Why we do not accept the result of our simulation study as evidence of a limitation of one method

I am doing a mixture model. I have established a new method using EM-algorithm. I have simulated data from a mixture model. Then, I applied my new method to the data. The result is very satisfying. ...
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3answers
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In Bishop's textbook, is the example of overfitting exaggerated?

Here, the data $x$ are randomly generated, and $t$ are generated by running $x$ through a function $\sin(2\pi x)$, then Gaussian noise is added. Bishop's text then tries to fit those data using a ...
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How can I understand the concept of a noise in machine learning?

In Bishop's book, one of the first examples is shown here Essentially, the data $x$ are randomly generated, and $t$ are generated by running $x$ through a function $\sin(2\pi x)$, then Gaussian ...
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1answer
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How to fit a superimposed distribution (\eg a Gaussian distribution + a Uniform distribution)

Suppose we have a set of independent observations of a random variable X, which is a Superimposition of two mutual independent random variables (i.e. X = Y + Z), Y follows a uniform distribution, ...
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1answer
191 views

R - how to estimate shape and scale parameters of Weibull distribution for claims development factors

I have a set of insurance data. Development factors fall with period, so follow Weibull distribution. I want to estimate Weibull parameters and smooth Development Factors. If I estimate parameters of ...
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Fitting wrong copula type to a real data set

I have developed a new mixture copula model. This model overcomes some limitation of copula models. I tested my new model on a simulation data. The model shows a superior result. My supervisor asked ...
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1answer
108 views

Inferring GMM parameters with Gibbs Sampling

On my book, "Machine Learning A Probabilistic Approach". It's stated that is straightforward to derive a Gibbs sampling algorithm to fit a mixture model, especially if we use conjugate priors. So ...
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71 views

How do I fit a cumulative Gaussian distribution in R? [closed]

I am trying to fit a cumulative Gaussian distribution function to my data, but I'm not sure how to do this. From what I understand, the fitting process tries to find the mean and standard deviation of ...
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28 views

Model fit for StMoMo

As a statistics newbie, I am trying to model mortality. I grabbed majority of the code from the package Vignette, and fitted the data. However, model fit does not seem to be great in my reproducible ...
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Compute log-likelihood from sum of squares?

I have fit a 2D Gaussian to a surface in Matlab and need to compute the log-likelihood of this fit. Can One use the sum of squares between the Gaussian model and the actual surface to compute the log-...
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AR(1)-GARCH(1,1). A bad fit with log likelihood?

Consider these two DCC models: ...
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3answers
183 views

Fit data to parametric distribution

I have data with nice bell-shaped histogram PDF. However, the Normal distribution fitting (by calculating mean and variance) does not work as the figure below. My question is that if there are other ...