### vect alea

parent ea02d6a8
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 ... ... @@ -48,7 +48,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ "# Densité, fonction de réparition, quantiles" "## Densité, fonction de réparition, quantiles" ] }, { ... ... @@ -199,7 +199,7 @@ "metadata": {}, "source": [ "***Exo:*** laquelle de ces deux représentations correpond à la fonction de répartition, à savoir: \n", "\t$x \\to P[ X\\leq x]$\n" "\t$x \\to P[ X\\leq x]$\n" ] }, { ... ... @@ -220,7 +220,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ "# Conseil sur les arguments facultatifs\n", "## Conseil python: les arguments facultatifs\n", "\n", "Considérons un appel d'une fonction de scipy :" ] ... ... @@ -267,7 +267,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ "# lois continues classiques" "## lois continues classiques" ] }, { ... ... @@ -284,7 +284,7 @@ "\n", "\n", "\n", "***Proposition :*** si $x\\to f(x)$ est la densité d'une va $X$, alors la densité de $\\sigma X + \\mu$ est:\n", "***Proposition :*** si $x\\to f(x)$ est la densité d'une va $X$, alors la densité de $\\sigma X + \\mu$ est:\n", "$$\n", " \\frac 1 \\sigma \\ f \\ \\Big( \\frac{ x-mu} \\sigma \\Big)\n", "$$\n", ... ... @@ -292,21 +292,18 @@ "\n", "*Astuce:* Pour ne pas s'encombrer la mémoire, retenez uniquement les densités des lois dans le cas $\\mu=0$ et $\\sigma=1$. Par exemple: \n", "\n", "$$\n", "\\begin{array}{cc}\n", "a & b \\\\\n", "\\end{array}\n", "$$\n", "\n", "\n", "| nom de la loi | simplifié | complète|\n", "| nom de la loi |        simplifié         |        complète         |\n", "|---------------|-----------| --------|\n", "| exponentielle | $\\exp(x) 1_{\\{x>0\\}}$ | $\\frac {1} {\\sigma} \\exp(- \\frac {x-\\mu } {\\sigma} )$ |\n", "\n", "| exponentielle | $e^{-x} 1_{\\{x>0\\}}$ | $\\frac {1} {\\sigma} \\exp(- \\frac {x-\\mu } {\\sigma} )$ |\n", "| normale | $\\frac {1} { \\sqrt {2 \\pi}} e^{-\\frac{1}{2} x^2}$ | ... |\n", "\n", "\n", " | normale | $\\frac {1} { \\sqrt {2 \\pi}} exp -x^2$ | ... |\n", "\n", "\n", "| aaa | bbb |\n", "|---|---|\n", "| $a$ | $b$ |\n", "\n", "\n", "\n", "\n", ... ... @@ -316,7 +313,7 @@ "$$\n", " \\mathbf E[\\phi( \\sigma X + mu )] = \\int \\phi( \\sigma x + \\mu) \\ f(x) \\ dx \n", "$$\n", "On effectue le changement de variable $\\sigma x + \\mu \\to y$ \n", "On effectue le changement de variable $\\sigma x + \\mu \\to y$ \n", "$$\n", " \\mathbf E[\\phi( \\sigma X + mu )] = \\int \\phi( y) \\ f(... ) \\ dy ... \n", "$$\n", ... ... @@ -471,7 +468,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ "# Lois à Queues lourdes\n", "## Lois à Queues lourdes\n", "\n", "Une loi est dites à queue lourde lorsque les v.a qui ont cette loi peuvent prendre, de temps en temps, des grandes valeurs positives ou négatives. Elle servent à modéliser des évènements rare et violent (ex: crue d'un fleuve). " ] ... ... @@ -598,7 +595,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ "# Relations entre les lois\n", "## Relations entre les lois\n", "\n", "\n", "Il est important de retenir les relations entre les principales lois, l'image ci-dessous peut vous aider à cela. Sinon, sur cette [page](http://www.math.wm.edu/~leemis/chart/UDR/UDR.html) contient encore plus de relations, ainsi que leur justifications mathématique. " ... ... @@ -610,18 +607,6 @@ "source": [ "![Relationships_among_some_of_univariate_probability_distributions](img/distributions.jpg)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { ... ... @@ -640,7 +625,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.0" "version": "3.6.5" } }, "nbformat": 4, ... ...
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 ... ... @@ -376,7 +376,7 @@ "step=(droite-gauche)/nb_batons\n", "weights=np.ones_like(X)/step/len(X)\n", "\n", "plt.hist(X,bins=nb_batons,weights=weights,range=[gauche,droite],edgecolor=\"k\")\n", "plt.hist(X,bins=bins,weights=weights,range=[gauche,droite],edgecolor=\"k\")\n", "x=np.linspace(gauche,droite,200)\n", "plt.plot(x, gaussian_density(x));" ] ... ...
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