# Questions tagged [mathematica]

Mathematica is a software package for symbolic mathematical computations.

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### how to distinguish negative shock or positive shock in TGARCH model?

IN the picture, how to know whether the yellow highlighted part exists or not? because the return of day 1000 drop from 0.02 to 0.01, so there was a negative shock, so l should keep the yellow ...
1 vote
51 views

### Number of simulated statistics more extreme than most extreme real data statistic

I have a distribution of $n_{obs}$ "real" data observations drawn from a normal distribution $X \sim N(\mu,\sigma^2)$, and a number $Q$ of simulated realizations of the same distribution, ...
14 views

If I have five variables, each with four sub-questions, In each sub-question, I have: 1 = I usually don't do this at all 2 = I usually do this a little bit 3 = I usually do this a medium amount 4 = I ...
11 views

### Hierarchial clustering given a list of banking syndicates

I have a list of banking syndicates (groups of banks), and I'm trying to do some hierarchical clustering on it to gather if there is some connection between them (e.g. if lots of syndicates share the ...
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35 views

### Are these data points decaying exponentially or as a power law?

0 I have a set of data points. The first coordinate is time and the second coordinate is energy. I am trying to figure out how the energy is decaying over time. Particularly, I have to find if it is ...
1 vote
326 views

### Residuals not normal due to random effects structure

I am new to mixed-effect models and statistics, and I need to do a project for my thesis using mixed-effect modeling techniques. My research aims to model how cardiovascular risk scores change over ...
46 views

### Would I use a one-tailed paired-sample t- test on this?

I am doing an assignment that tests whether acceptance and commitment therapy is beneficial for social anxiety disorder. With an experimental and controlled group. I just need to know what test I ...
164 views

### Prove E[Y|X] = f(X)

I have a model $Y = f(X) + \epsilon$ where $\epsilon$ is independent of $X$ and $\mathbb{E}[\epsilon]=0, \mathbb{E}\left[\epsilon^2\right]=\sigma^2$. Show that $$f(X)=\mathbb{E}[Y \mid X]$$ This is ...
83 views

### Maximum Uncertainty in Normal Distribution

While reading Goodfellow's Deep Learning Book, I came across the below fact about Normal Distribution. I am not sure I have understood what led to this conclusion, Can someone help with it? "Out ...
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473 views

### How can Hinge loss be upper bound of the 0-1 loss?

I just have a question and I did not find clear explanation, hinge loss is upper bound of 0-1 loss, so does this mean upper bound regard to a single point loss such as 0 or 1 ?!. So, for example the 0-...
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1 vote
1k views

### How do we update the parameters (weights) in recurrent neural networks?

In RNNs, how do we update the weights? I have following understanding of RNNs: Parameters are shared across all time-steps, i.e., $$S_t = \tanh(U X_t + W S_{t-1} )$$ $$Y_k = \text{softmax}(V S_t)$$ ...
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1 vote
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### How to simplify the understanding behind Hypothesis Testing? [duplicate]

Quote recently, I have trying to understand this confusing idea of Hypothesis testing. Although I am pretty much clear with the way it works, that is: Choosing a test statistic Then choosing a Null ...
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1 vote
83 views

### What mathematical background do I need to do research in field of deep learning

I am familiar with few deep learning models and I understand how (little bit why) CNN/RNN works. But I still cannot make sense of new research papers. I want to dive deeper into field of deep learning ...
172 views

### mathematical proof that if the vectors 𝑞⃗ and 𝑑𝑖 all are normalized unit vectors [closed]

In a vector space model when we are given a query as a vector 𝑞⃗ and documents 𝑑1 , 𝑑2 …, we usually rank the documents in relevance to the query vector using cosine similarity. Show by a ...
1 vote
128 views

### Is there any relationship between two normalized gamma distributions?

Consider two normalized gamma distribution functions $\frac{\Gamma(x,y)}{\Gamma(x)}$ and $\frac{\Gamma(nx,ny)}{\Gamma(nx)}$ where $n$ is a positive integer value. Is there any relationship between the ...
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1 vote
99 views

### How can I incrementally calculate the 4 central moments in statistics (mean, standard deviation, skewness and curtosis) when a value is removed?

I'm incrementally calculating the 4 central moments. When a value x is added and n, M1, M2, M3 and M4 are some predefined values, I'm using the following algorithm: ...
1 vote
34 views

### How to expand $\text{erf}\bigg(\frac{(ax-b)}{\sqrt{2}}\bigg) = \text{erf}\bigg(\frac{ax}{\sqrt{2}}\bigg) + \text{some_value}$?

The error function is defined as, $$\text{erf}\bigg(\frac{(ax-b)}{\sqrt{2}}\bigg) = \frac{2}{\sqrt{\pi}}\int_{0}^{\frac{(ax-b)}{\sqrt{2}}} e^{-t^{2}/2}dt$$. My question is how to expand the above ...
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### How to produce synthetic (fake) data knowing the correct fit parameters?

For cross-checking purposes, if I want to check that a NonlinearModelFit performed in Mathematica is producing the correct standard errors, I would need to produce simulated data based on the fitted ...
128 views

### how to find domain of marginal pdf when its two variables domain are dependent

I have a pdf $f(x,y)=1/π, 0< x^2+ y^2 <1$； 0, e.w. Here, we can see $-\sqrt{1-x^2} < y < \sqrt{1-x^2}$ So, the marginal pdf of $X$ is $$\int_{-\sqrt{1-x^2}}^\sqrt{1-x^2} 1/πy \, dy\,.$$ ...
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### How to derive the gradient for SSE cost function in Adaline?

I started learning machine learning and have some troubles in understanding derive rules for the gradient of cost function in particular I can't understand how sum(wjxj) transformed to -xj. I tried to ...
417 views

### Linear Regression Coefficient Interpretation [closed]

I have a regression problem: regress y on x1 x2 y: Sales revenue, x1: is_holiday (dummy variable), x2: another continuous variable (note that this is just the ...
1 vote
392 views

### Deriving parameters of an extreme value distribution from an initial distribution for finite n

Background: For my research I've been trying to model brittle fracture mathematically. The basic concept is that a brittle materials fail because already existing small defects such as small cracks ...
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### Choosing center of histogram bins for fitting

I have a bimodal distribution, and if plotted with Mathematica it looks like this: Now, the lowest value from the actual data is 8196 and 690720, but as seen in the plot, Mathematica lets the data ...
1k views

### Uniform Density Function

As we know the uniform probability density function is f(x)=1/(b-a) if i find the density function and area of this uniform distribution between (0, 1/2) then it would be f(x)=1/(1/2-0) f(x)=2 ...
1 vote
238 views

### Find $\mathbb{E} \bigg[ \frac{\textbf{h}^{H} \textbf{y}\textbf{y}^{H} \textbf{h}}{ \| \textbf{y} \|^{4} } \bigg]$ with Mathematica? [duplicate]

Considering the following complex random vectors (Complex Gaussian random variables): \begin{align} \textbf{h} &= [h_{1}, h_{2}, \ldots, h_{M}]^{T}\ \ \sim \mathcal{CN}(\textbf{0}_{M},d\textbf{I}_{...
299 views

### Book recommendation for undergraduate stats with Mathematica

Having just completed my Bachelor with a major in math and physics, I am aware that due to my chosen specialisation, I lack a good training and exposure in statistics beyond the first year. Could ...
93 views

### $X_1, X_2$ are IID $N(0,1)$. Find Cov($X_1$, $X_1 X_2$).

Two variables $X_1, X_2$ are independent and identically distributed as $N(0,1)$. I need to find Cov($X_1$, $X_1 X_2$). Thanks!
2k views

### How to read/visualise this confusion matrix?

I was offered a confusion matrix, which is called Parametrised 5x5 confusion matrix by authors where I extracted the values and where the diagonal has the correct results (0 in all); the results are ...
2k views

### How to implement density-based clustering?

I’m looking to implement density-based clustering with R or Mathematica on a giant file (600,000 points on a 3 billion x 3 billion plane). Is DBSCAN the right method for data that is this sparse? I am ...
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1 vote
64 views

### Comparing two crash rates and determine if they are statistically significant

Let's say I have two version of an App. Version A goes to 1000 users and Version B goes to 800 users. A month into testing, I have all of my crash data and crash percentages for both of the versions. ...
6k views

### Comparing two datasets with same variable

thanks in advance for anyone taking the time to read/answer this. I am comparing a ground-sourced dataset versus a satellite-sourced dataset for weather conditions, such as temperature. Both sets are ...
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1 vote
3k views

### On what basis we are evaluating variance is high or low? [closed]

I am having a below case where N = 300 , Mean = 67 and SD = 30. With the above data we can say the variance is high because of SD = 30. My question is how we are defining it as high on what basis we ...
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1 vote
51 views

### Measuring Autocorrelation in Tail Events

I have a single time series of financial data (stock index returns) and would like to study the autocorrelation among (log-)returns that are classified as "extreme", for example via exceedance of a ...
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### Why fitting does not find the true best point

I fitting an expression of the form: $s(t)=\frac{1}{1+\exp[a+\sum_k b_k x_k(t)]}$ Where $a$ and $b_k$ are fitting parameters and $x_k(t)$ an input time series. I have $k=1,...,N$ different types of ...
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510 views

### Fitting one set of data with two functions

I have a set of data (42 points): ...
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### What is a good test for comparing frequency counts between two groups?

I am looking for statistical methods used to compare frequency of observations between two groups. I have two geographical locations with data on different soil types present. for example, my data ...
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1 vote
35 views

### Visualising n vectors of length n in a periodic fashion

I'm currently working on a specific problem in a periodic structure, for which I obtain a set of eigenvectors that I would like to plot. It is probably easiest if I give you an explicit example, then ...
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1 vote
234 views

### Samples from a multivariate t distribution

Hi I have the following problem. I draw a sample of a multivariate t-distribution with some fixed covariance matrix, so that the realizations are correlated, and $\nu=4$. Now I repeat this $n$ times, ...
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1k views

### software library to compute KL divergence?

Are there any software libraries that compute KL divergences in closed form, that also give the derivatives of the KL divergence wrt the distributions' parameters? I'm using Julia, so it's ...
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### How can I compute the lower and upper bounds of a confidence interval in a linear regression problem?

I am completing a university statistics assignment on the Mathematica program, and this is the initial question: "The Medical Research Council wanted to evaluate the effects of different dosages of a ...
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771 views

### PDF of a sum of dependent variables

This is a direct continuation of my recent question. The thing that I actually want to get is the distribution of $a+d+\sqrt{(a-d)^2+4bc}$, where $a,b,c,d$ are uniform in $[0,1]$. Now, the ...
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### What's the distribution of $(a-d)^2+4bc$, where $a,b,c,d$ are uniform distributions?

I have four independent uniformly distributed variables $a,b,c,d$, each in $[0,1]$. I want to calculate the distribution of $(a-d)^2+4bc$. I computed the distribution of $u_2=4bc$ to be f_2(u_2)=-\...
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863 views

### Neural Network - Classification from Time series

I'm a .Net programmer who is fairly new to neural networks, but I know some of the concepts. I have connected .Net to my copy of Mathematica 10 This is a classification Our business problem is ...
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### Mathematica's random number generator deviating from binomial probability?

So, let's say you flip a coin 10 times, and call that 1 "event". If you run, 1,000,000 of these "events", what is the proportion of events that have heads between 0.4 and 0.6? Binomial probability ...
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### How can I fix a poor nonlinear curve fit?

I was trying calculating Fourier transform of some rings. as follow: By directly calculating of model as several rings, the result showed different from the the experimental ones. So I tried to get ...
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1 vote
911 views

### Problem with multivariate lognormal distribution in R [closed]

I'm using the R package compositions for the multivariate lognormal distribution. This is the only package I found that supports it. However I'm not sure how this ...
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### Difference in output from mvtnorm and Mathematica/Java [closed]

Let $a \sim\mathcal{N}(6.532056,0.06532056)$,$b \sim\mathcal{N}(8.390961,0.08390961)$ and $c \sim\mathcal{N}(8.736566,0.08736566)$. We use $\mathcal{N}(\mu,\sigma^2)$ notation unless specified ...
1 vote
495 views

### Unkown 6-sided dice. After 600 rolls frequency for all sides exactly equal. What is the chance, that rolling "6" with this dice has frequency > 1/6?

Although it is unknown dice, the symmetry of the evidence tells us, that we can treat the dice as fair, so the chance should be exactly 50%. But if we simulate it by hand, the result is less then 50%:...
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I'm looking for visualization ideas for the following data: I have a $10\times 12$ grid of points $(x_i,m_j)$, where the $x_i$ are a set of distances (e.g. 1,2,..., 10 m) and the $m_j$ are the ...