Animations : alphabetical order

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

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

LISTE OF THE 61 ANIMATIONS (in alphabetical order)

Note : an animation may appear in several places under different names.

Asymptotic distribution	Asymptotic distribution of the statistic of a Likelihood Ratio Test.
Barycenter	The number of points, their weights and their positions can be changed. The barycenter of the projections is the projection of the barycenter.
Beta distribution	Shapes of the Beta distribution depending on the values of the two parameters.
Bias	The sample mean is an unbiased estimator of the distribution mean.
Bias	Unbiased estimator, UMVUE, lowest MSE.
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.
Chi-2 statistic	Comparison of the behaviors and performances of Pearson's Chi-2 statistic and Wilks' G² statistic.
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 independent exponential 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.
Exponential distribution	Distribution of the record values.
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.
Fisher-Irwin test	The distribution of two independent binomial rvs conditionally to their sum is hypergeometric.
Gamma distribution	Shape depends on the adjustable parameters.
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.
Likelihood Ratio Test	Asymptotic distribution of the statistic of a Likelihood Ratio Test.
Least squares line	Least Squares Line (LSL) manually adjustable on a sample. Sample size and "noise" are adjustable.
Mahalanobis distance	Distribution of the squared Mahalanobis distance (bivariate normal distribution).
Marginal distribution	Distributions of the product and ratio of two independent and uniformly distributed r.v. as marginal distibutions of their joint distribution.
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 of a sample	Mean (or "average") of a sample whose observations are manually adjustable.
Mean Square Error	The model MSE depends on the number of parameters.
Mean (normal distribution)	Distribution of the sample mean of the normal distribution is normal.
Mean (exponential distribution)	Distribution of the sample mean of the exponential distibution.
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 an arbitrary distribution (including uniform as a special case). Sample size and rank of the statistic are adjustable.
Poisson distribution	Comparison of the Poisson distribution and the Binomial distribution. Sample size, Poisson's Lambda et binomial p are adjustable.
Poisson distribution	Simulation by drawing observations from an exponential distribution.
Poisson process	Poisson process with adjustable rate.
Probability density	Relationship between "Probability density function" and "Distribution function".
Probability Integral Transformation	Building of an arbitrary density, and simulating it by Probability Integral Transformation.
Record values	Distributions of the recortd values of the exponential and uniform distributions.
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.
t test	Distribution of the test statistic for two independent samples.
Uniform distribution	Four illustrated problems based on the uniform distribution.
Uniform distribution	Distributions of the order statistics of the uniform distribution.
Uniform distribution	Distribution of the record values.
Uniform distribution	Distributions of the product and ratio of two independent and uniformly distributed r.v. as marginal distibutions of their joint 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.
Wilks' G² statistic	Comparison of the behaviors and performances of Pearson's Chi-2 statistic and Wilks' G² statistic.

Note : an animation may appear in several places under different names.

The "Book of Animations" on your computer