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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 understand the results of nonlinear mixed-effects regression model

I have some data, obtained from 4 different groups. Each repeat is some 4 parametric sigmoid. I need to fit the data to sigmoidal function and answer the question, whether sigmoids are different ...
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29 views

How to solve systems of linear equations with random variables? How to identify model parameters?

I want to learn know how to solve systems of linear equations with randomness. Example of a deterministic version of the sort of problem I want to solve: ...
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40 views

Bayesian networks with continuous variables in Python [closed]

I am trying to create a Bayesian network model (Probabilistic graphical model) in Python, that can handle continuous data. I have tried using pgmpy, but the 'fit' function in pgmpy has not yet been ...
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15 views

Correct Interpretation of copula contour plots

Going into exploratory data analysis with the intention of fitting copula models, I was looking at the famous copula and they mention here that either contour or 3D ...
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41 views

How to fit a distribution to binned values that come from administrative data?

Fitting a distribution to data (e.g. with maximum likelihood), or testing goodness of fit (e.g. with Kolmogorov-Smirnov) assumes that the data are randomly drawn from a population. But what if the ...
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43 views

Showing that $\sum_{i=1}^n y_i = \sum_{i=1}^n \hat{y_i}$

Exercise : Prove that for the Generalized Linear Model with a constant intercept $b_0$, the sum of the observed values equals the sum of the fitted values : $$\sum_{i=1}^n y_i = \sum_{i=1}^n \hat{...
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8 views

fitting for random remnants of known perturbers

I have the following problem: We try to analysis spectra. In our data analysis, we have to correct for perturbers that occur always at the same frequency and can be approximated by a Gaussian of ...
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1answer
20 views

How do I best use a fit statistic like chi-squared fit for a model that predicts two independent sets of measurements?

I have a model $M(\vec{x})$ for a vector of model parameters $\vec{x}$ that predicts two sets of measurements that I have taken - $v(h)$ and $L(h)$. The two independent data sets each have their own ...
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72 views

Best estimation of a fitting parameter to measured data

My goal is to estimate a parameter $\alpha_1 = (\alpha_{11}, \alpha_{12})$ which provides the best fit of certain measured data (a readout of some currents in a set of positions for a set of loads) to ...
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1answer
27 views

Are there theoretical reasons for choosing between similar distributions?

I'm interested in estimating the distributions of a few skewed datasets, for example extreme heat, and extreme rainfall. There are many distributions that can be fit to these kinds of data, for ...
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2answers
53 views

How to fit laplace/exponential distribution to cosine similarities?

I am a computational biologist with little experience fitting data. I'm trying to fit a distribution of cosine similarities computed between sparse matrices. The goal is to be able use this ...
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18 views

Can I use this distribution to model my data according to these plots?

I used the Anderson-Darling and the KS tests to decide whether my data and the distribution fitted on my data has the same distribution. Both tests rejects the null hypothesis. However when I look at ...
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1answer
32 views

Why random numbers from fitted distribution do not have the same distribution as the sample data?

I have a data set and I would like to fit a t distribution on it. I use R or Python to feed into my data, and I get the degrees of freedom, the location and the scale parameters. After that, I ...
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26 views

How to get specific terms of a polynomial function in a regression?

I want to simplify data from a complex modell like: fit <- lm(z ~ poly(a,4)*poly(b,5)*poly(c,6), data = somewhat) As I don't know which terms of the complete ...
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11 views

Fitting t distribution to data - intuition behind the degrees of freedom [duplicate]

If I use the fitdistr function in R, I get that the fitting distribution has 5 degrees of freedom. What does that mean in practice? Isn't the $df$ for $t$ ...
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30 views

Average of two fits vs fit of a combined data

Lets say I have data from two independent simulations. One of them look like this: The fitted curve is done by minimizing absolute difference between each data point and the curve. The fit ...
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28 views

Finding a distribution that fits different observations of data

I am observing session lengths on a network. I want to fit a distribution to the data that I have collected. I have data from two different observations (about a month apart). The plot below shows ...
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1answer
49 views

Fitting data to a log-normal distribution [duplicate]

For a simulation study I've been trying to find an appropriate distribution for job handling times in R. I have a very large dataset of 77010 records (handling time in seconds). I've been exploring ...
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1answer
23 views

What is the number of iterations used to estimate the ARMA coefficient

If we are using the LSE "least square error" equation for getting the AR and MA terms: by getting the LSE in function of the coefficients and differencing it then equating it to zero.This yields ...
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1answer
93 views

Fit Hawkes process to 1d data using python package TICK

How can one fit the 1-dimensional Hawkes process with exponential kernel to the experimental 1d dataset (t1,t2,t3...tn) and check the goodness-of-fit via tick python3 package? I found on official ...
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1answer
78 views

Fit a parametrized distribution on a set of quantiles

first of all, I'm not a statistician nor a data scientist, but a software developer. Thus, although I do have some (old) knowledge in statistics and probabilities, my vocabulary may not be very ...
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1answer
27 views

Why are mixed effect methods more effective when data are limited

In the study in here, it is said that mixed effects models are better in estimating parameters of a ODE system when there is only very small number of data to estimate the parameters. So, in a ...
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38 views

Fitting a distribution to data given only the tails? Fitting normal distribution from only the 90th-99th percentile of data [duplicate]

I'm trying something out in R and I'm curious how one would go about doing this. Let's say I have a sample of Americans and their income, furthermore I know that they are in the 90th-99th percentile ...
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1answer
45 views

test if two linear fits are different

I have time-dependent data from experiments done by two different labs. Lab1 has measurements at 60 different time-points. Lab2 has measurements at 40 different time-points (within the same range as ...
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2answers
479 views

Formal definition of the qqline used in a Q-Q plot

I'm doing some distribution fitting work and I'm looking at Q-Q plots and how they can be used visually to interpret goodness of fit. My data is heavy-tailed so I am looking at Weibull, log-normal, ...
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44 views

Generalized Additive Models: How to fit models with the LMS method by Cole?

I have some problems to understand the univariate generalized models that were proposed by Cole (1992). My question is how the fitting procedure works described in the appendix. More specific, how to ...
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27 views

Does conditional intensity function of some model must perfectly match with data intensity if model is true?

I consider some emperical dataset characterized by a single parameter - the arrival times of events {$t_0,t_1,t_2,...,t_i$} as is commonly adopted for point processes. The Hawkes model is tested for ...
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28 views

Fitting a system that transits between two time varying states

I have a system that transit between two different states. Each state output varies linearly with time, given by m*t+c, where both lines intersect the x axis in the same point. The output of this ...
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19 views

Fit Correction on known distributions

I'm looking for a way of correcting a linear fit through data. The scenario is the following: In red you have data points, they are based on uniformly distributed points on the black straight line ...
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1answer
52 views

Dealing with heteroscedasticity when dependent variable is already log-transformed

I have already log-transformed the dependent variable but there is still heteroscedasticity in the residual-fitted plot. What one usually does in situations like ...
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1answer
68 views

What is a positively skewed distribution that can include zero?

I'm modelling data from a behavioural task. Participants do a few hundred trials. On each trial, they see a sequence of letters at a point on the screen and one of these letters appears surrounded by ...
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15 views

Fitting regime switching model to binary time series

I have a binary time series $X_t$ that I'd like to fit. It clearly has long memory effects (high Hurst exponent), and I believe that it is generated by a Bernoulli process where the probability ...
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85 views

How to estimate passengers destinations from flightradar data?

We have a graph with vertices corresponding to airports and edges corresponding to flights between those airports. On edge between airports A and B we have and number of passengers transferred from A ...
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55 views

fitting curve to my data and calculating fwhm

Hello and thank you in advance for your inputs. I am trying to find a model in R that will give me curves that fit my data. I am aiming for 2 peaks (i am thinking of normal distributions but might be ...
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22 views

Assessing the fit of a state-space model in JAGS

I've been fitting a relatively complicated state-space model in JAGS and I want to do some basic model comparisons, including dropping parameters one at a time to assess their influence on the fit. ...
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19 views

MCMC “best fit” determination for highly correlated/covariant parameters

People often get the "best fit" by finding the median of each dimension. When posteriors are highly non-gaussian, and weirdly covariant, this can fail horribly. For example, here's a schematic ...
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30 views

Finding an Analytical Relationship Between Variables

I have a spreadsheet read from a metheorological system with a simple model embedded. I solved the most variables by simple inspection and through related literature, but unfortunately, the literature ...
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32 views

Fitting a Multivariate Normal Model

Is there a standard method for fitting multivariate normal models where $\mu(\theta)$ and $\Sigma(\theta)$ are nonlinear functions of the model parameters? In my case I have a single vector of ...
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32 views

Punzi terms and change of basis

I've collected a datasample with both signal and background events to estimate some parameters of interest, $\lambda$, using a unbinned maximum log-likelihood fit. The signal PDF is conditionaly ...
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6 views

Non-Linear Fit Preserving Normalisation

I have a problem I have been struggling with for a while: I need to carry out a non-linear fit (and this is the easy part). I have a set of discrete values {x1,x2...xN} and the corresponding {y1, y2......
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2answers
132 views

Maximum likelihood and Gumbel distribution. Does the likelihood have a global maximum?

It appears to me that if I move the mode $u$ more to the negative and increase the scale parameter $\alpha$, one can get always a higher likelihood. If this is true, is there a limit of the likelihood?...
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1answer
146 views

How to improve fit of distribution to data

I'm trying to fit one of common expenential distributions to data using histfit. However it seems that results aren't as good as expected - it seems that peak should be higher. Histograms presents ...
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39 views

Which regression to choose for this distribution?

I started to work with linear models recently and have a few questions about LMs and GLMs. My target looks like this (see below) and I have approx. 20 features. Can somebody please confirm or ...
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43 views

Easy Distribution Fitting Techniques?

This is a made-up scenario that I am creating, but if I can figure out how to figure out a problem for this scenario, it would help me better understand distribution fitting. Say you and a friend are ...
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42 views

Copulas - what marginals can I use? (theory)

For my research I am using various copulas and I fit different marginal distributions to my data. I've studied the topic of inter-variable dependency quite a bit, however, I do not recall the ...
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203 views

Fitting higher order Markov chains in R

For $n$ individuals I observe their states at fixed times. So I have $n$ observations of a data generating Markov chain. Using the markovchain-package I then can fit a time-homogeneous Markov chain ...
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2answers
408 views

How to transform a frequency data in to normal distribution?

I have this set of data: 0 700 1 350 2 250 3 300 4 150 5 145 6 150 7 147 being the first column about the type of the event (zero days, onde day, ...
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31 views

Modelling Payment Receipts, High Skewness & Kurtosis

I have the following distribution of payment receipts with respect to their due date. Anything less than zero is prepaid and after zero is late. How should I formulate my basic approach to modelling ...
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48 views

Model fitting when correlated data errors. Help computing the co-variance matrix for minimizing generalized Chi squared

I am working with 30 data elements $x_i$ from a model. I consider the data $x_i$ to have zero error. What I want to do, is to fit a model to the following transformation of this data: $y_i = y(x_{i-1}...
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36 views

Interpret the result of a fitted non-stationary Gumbel model

I have a dataset on wildfires that I fitted to a Gumbel distribution with a set of covariates (using the gevrFit function in the eva package in R). The result of ...