The "Book of Animations"
on your computer............  

The Animations ordered by
Themes........................

          LISTE OF THE 49 ANIMATIONS   (by alphabetical order)

Barycenter

The number of points, their weights and their positions can be changed.

The barycenter of the projections is the projection of the barycenter.

Bias

The sample mean is an unbiased estimator of the distribution mean.

Bias-variance tradeoff

The model MSE depends on the number of parameters.

Binomial  (Distribution)

Simulation of the binomial distribution B(n, p). Sample size n and probability p are adjustable.

Binomial  (Calculator)

Binomial calculator. Calculates probabilities and cumulated probabilities.

n and p are adjustable.

Binomial   (indépendent)

Distribution of two independent binomial variables conditionally to their sum (leading to the Fisher-Irwin test).

Binormal  (Distribution)

Standard deviations and correlation coefficient of the marginals are adjustable.

Bootstrap

Bootstrap estimation of the mean and median of a custom-made distribution.

Cauchy

The Cauchy distribution as the distribution of "impacts" or as the ratio of two independent normal distributions.

Distribution of the sample mean is the same Cauchy as the original distribution for any sample size.

Central Limit Theorem

Distribution of the sample mean of an arbitrary distribution. As the sample size is made larger, this distribution is more and more "normal-like".

Chi-2 distribution

Simulation of the Chi-2 distribution. Sample size is adjustable.

Confidence interval

Position of the confidence interval as a function of the sample drawn from a normal distribution. Sample size and confidence level are adjustable.

Covariance and Correlation Coefficient

Sample is modified so as to maintain the Correlation Coefficient constant.

Positions of points are individually adjustable.

Covariance matrix

Positions of points in the cloud are in individually adjustable. Covariance matrix, Diagonalized Covariance matrix and Principal Components are updated in real time.

Estimators  (independent)

Best linear combination of independent estimators.

Exponential distribution

Basic properties of the exponential distribution.

Exponential distribution

Manual tuning of an exponential to the ML for a sample.
Progressive histogram of the sample mean. Unbiasedness of the sample mean.

Exponential distribution

Memoryless property (weak) of the exponential distribution.

Exponential distribution

Strong memoryless property of the exponential distribution.

Exponential distribution

Probability for a machine to be the first one to break down.

Exponential distribution

Distribution of the min of several independentexponential random variables.

Exponential distribution

Distribution of the spacings of the exponential distribution.
Expectation of the max of iid exponential r.v..

Exponential distribution

Distributions of X₁ and of X₂ conditionally to X₁ < X₂.

Fisher's distribution

Distribution of the ratio of the estimated variances from two samples generated by two independent normal distributions. Sample sizes are adjustable.

Fisher's discriminant

Direction of largest separation of the projections of two classes.

Gamma distribution

Distribution of the sum of i.i.d. exponential random variables.

Geometric distribution

Geometric distribution, p and the number of bins adjustable.

Histogram

Instability of a histogram as a function of sample size and bin size. Bias-variance tradeoff.

Number of bins and sample size adjustable.

Hypergeometric

Hypergeometric distribution. All key parameters are adjustable.

Inertia  (of a cloud of points)

Inertia with respect to an arbitrary point. Directions of largest spread and of largest projected inertia. Variation of the projected inertia along an an adjustable direction.

The positions and weights of the points are individually adjustable.

Intercept

Distribution of the intercept in Simple Linear Regression under the standard hypothesis.

Kullbak-Leibler

Kullbak-Leibler distance between two adjustable normal distributions.

Kullbak-Leibler distance between two samples whose observations are individually adjustable.

Least squares line

Least Squares Line (LSL) manually adjustable on a sample. Sample size and "noise" are adjustable.

Maximuml likelihood
(Exponential distribution)

Manual tuning of an exponential to the ML for a given sample.
Progressive histogram of the sample mean. Unbiasedness of the sample mean.

Maximuml likelihood
(Normal distribution)

Manual tuning of a normal distribution  for a sample.

Mean Square Error

The model MSE depends on the number of parameters.

Monte-Carlo simulation

Estimating the area of an irregular region in the plane.

Calculating p :

     * Area of a disk.

     * Buffon's needle.

Negative binomial

Simulation of the negative binomial distribution. p and sample size are adjustable.

Normal distribution

Sample mean is normally distributed. Distribution variance and sample size are adjustable.

Normal distribution

Manual tuning of a normal distribution to its Maximum Likelihood for a given sample.

Normal distribution

What is the distribution obtained by making the mean of a normal distribution
a normal r.v. ?

Normal bivariate

Standard deviations and correlation coefficient of the marginals are adjustable.

Order statistics

Distribution of the order statistics of the uniform distribution. The rank of the order statistic can be chosen.

Poisson

Comparison of the Poisson distribution and the Binomial distribution. Sample size, Poisson's Lambda et binomial p are adjustable.

Probability density

Relationship between "Probability density function" and "Distribution function".

Simulation by Monte-Carlo

Estimating the area of an irregular region in the plane.

Calculating p :

     * Area of a disk.

     * Buffon's needle.

Slope

Distribution of the Slope of the Least Squares Line in Simple Linear Regression under the standard hypothesis.

Standard deviation

Graphic representation of the Standard-Deviation. Number of points and their individual positions are adjustable.

Standardization

Observations in the sample can be positioned individually. The standardized sample is updated in real time.

Student's t distribution

Student's t distribution. Sample size is adjustable.

Uniform distribution

Four illustrated problems based on the uniform distribution.

Weighted least squares

Comparison between the LSL and the ponderated LSL. Comparison of the standard deviations of the prediction errors for an adustable value of the predictor.

The "Book of Animations" on your computer