{"id":25206,"date":"2025-03-04T15:57:30","date_gmt":"2025-03-04T14:57:30","guid":{"rendered":"https:\/\/qooant.com\/distribucion-normal-y-lognormal\/"},"modified":"2025-03-06T15:19:31","modified_gmt":"2025-03-06T14:19:31","slug":"distribucion-normal-y-lognormal","status":"publish","type":"post","link":"https:\/\/qooant.com\/es\/distribucion-normal-y-lognormal\/","title":{"rendered":"Distribuci\u00f3n normal y lognormal"},"content":{"rendered":"

Para explicar este apartado partiremos de un caso pr\u00e1ctico: Cogemos como ejemplo el movimiento del EURUSD y elegimos como per\u00edodo de c\u00e1lculo el de una hora.<\/span><\/p>\n

Debemos tener en cuenta que podr\u00edamos haber cogido cualquier per\u00edodo para hacer el ejemplo (un minuto, 5 minutos, una semana, etc.).<\/span><\/p>\n

Cogemos como precio la media entre el precio ask y el precio bid.<\/span><\/p>\n

Calculamos la variaci\u00f3n horaria del movimiento del EURUSD de un d\u00eda cualquiera.<\/span><\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
<\/td>\n<\/td>\n<\/td>\n<\/td>\nVariaci\u00f3n horaria<\/b><\/td>\n<\/tr>\n
Hora<\/b><\/td>\nAsk<\/b><\/td>\nBid<\/b><\/td>\nPrecio<\/b><\/td>\nEn precio<\/b><\/td>\nEn Pips<\/b><\/td>\n<\/tr>\n
1:00:00<\/span><\/td>\n1,08117<\/span><\/td>\n1,08115<\/span><\/td>\n1,08116<\/span><\/td>\n0,00000<\/span><\/td>\n0<\/span><\/td>\n<\/tr>\n
2:00:00<\/span><\/td>\n1,08215<\/span><\/td>\n1,08212<\/span><\/td>\n1,08214<\/span><\/td>\n0,00097<\/span><\/td>\n97,5<\/span><\/td>\n<\/tr>\n
3:00:00<\/span><\/td>\n1,08187<\/span><\/td>\n1,08184<\/span><\/td>\n1,08186<\/span><\/td>\n-0,00028<\/span><\/td>\n-28<\/span><\/td>\n<\/tr>\n
4:00:00<\/span><\/td>\n1,08171<\/span><\/td>\n1,08170<\/span><\/td>\n1,08171<\/span><\/td>\n-0,00015<\/span><\/td>\n-15<\/span><\/td>\n<\/tr>\n
5:00:00<\/span><\/td>\n1,08140<\/span><\/td>\n1,08137<\/span><\/td>\n1,08139<\/span><\/td>\n-0,00032<\/span><\/td>\n-32<\/span><\/td>\n<\/tr>\n
6:00:00<\/span><\/td>\n1,08124<\/span><\/td>\n1,08122<\/span><\/td>\n1,08123<\/span><\/td>\n-0,00015<\/span><\/td>\n-15,5<\/span><\/td>\n<\/tr>\n
7:00:00<\/span><\/td>\n1,08091<\/span><\/td>\n1,08091<\/span><\/td>\n1,08091<\/span><\/td>\n-0,00032<\/span><\/td>\n-32<\/span><\/td>\n<\/tr>\n
8:00:00<\/span><\/td>\n1,08127<\/span><\/td>\n1,08126<\/span><\/td>\n1,08127<\/span><\/td>\n0,00036<\/span><\/td>\n35,5<\/span><\/td>\n<\/tr>\n
9:00:00<\/span><\/td>\n1,08112<\/span><\/td>\n1,08110<\/span><\/td>\n1,08111<\/span><\/td>\n-0,00016<\/span><\/td>\n-15,5<\/span><\/td>\n<\/tr>\n
10:00:00<\/span><\/td>\n1,08162<\/span><\/td>\n1,08156<\/span><\/td>\n1,08159<\/span><\/td>\n0,00048<\/span><\/td>\n48<\/span><\/td>\n<\/tr>\n
11:00:00<\/span><\/td>\n1,08108<\/span><\/td>\n1,08105<\/span><\/td>\n1,08107<\/span><\/td>\n-0,00052<\/span><\/td>\n-52,5<\/span><\/td>\n<\/tr>\n
12:00:00<\/span><\/td>\n1,08189<\/span><\/td>\n1,08187<\/span><\/td>\n1,08188<\/span><\/td>\n0,00081<\/span><\/td>\n81,5<\/span><\/td>\n<\/tr>\n
13:00:00<\/span><\/td>\n1,08132<\/span><\/td>\n1,08129<\/span><\/td>\n1,08131<\/span><\/td>\n-0,00057<\/span><\/td>\n-57,5<\/span><\/td>\n<\/tr>\n
14:00:00<\/span><\/td>\n1,08129<\/span><\/td>\n1,08127<\/span><\/td>\n1,08128<\/span><\/td>\n-0,00002<\/span><\/td>\n-2,5<\/span><\/td>\n<\/tr>\n
15:00:00<\/span><\/td>\n1,08221<\/span><\/td>\n1,08199<\/span><\/td>\n1,08210<\/span><\/td>\n0,00082<\/span><\/td>\n82<\/span><\/td>\n<\/tr>\n
16:00:00<\/span><\/td>\n1,08356<\/span><\/td>\n1,08354<\/span><\/td>\n1,08355<\/span><\/td>\n0,00145<\/span><\/td>\n145<\/span><\/td>\n<\/tr>\n
17:00:00<\/span><\/td>\n1,08308<\/span><\/td>\n1,08306<\/span><\/td>\n1,08307<\/span><\/td>\n-0,00048<\/span><\/td>\n-48<\/span><\/td>\n<\/tr>\n
18:00:00<\/span><\/td>\n1,08379<\/span><\/td>\n1,08376<\/span><\/td>\n1,08378<\/span><\/td>\n0,00071<\/span><\/td>\n70,5<\/span><\/td>\n<\/tr>\n
19:00:00<\/span><\/td>\n1,08408<\/span><\/td>\n1,08406<\/span><\/td>\n1,08407<\/span><\/td>\n0,00029<\/span><\/td>\n29,5<\/span><\/td>\n<\/tr>\n
20:00:00<\/span><\/td>\n1,08415<\/span><\/td>\n1,08412<\/span><\/td>\n1,08414<\/span><\/td>\n0,00006<\/span><\/td>\n6,5<\/span><\/td>\n<\/tr>\n
21:00:00<\/span><\/td>\n1,08374<\/span><\/td>\n1,08373<\/span><\/td>\n1,08374<\/span><\/td>\n-0,00040<\/span><\/td>\n-40<\/span><\/td>\n<\/tr>\n
22:00:00<\/span><\/td>\n1,08408<\/span><\/td>\n1,08372<\/span><\/td>\n1,08390<\/span><\/td>\n0,00016<\/span><\/td>\n16,5<\/span><\/td>\n<\/tr>\n
23:00:00<\/span><\/td>\n1,08407<\/span><\/td>\n1,08395<\/span><\/td>\n1,08401<\/span><\/td>\n0,00011<\/span><\/td>\n11<\/span><\/td>\n<\/tr>\n
0:00:00<\/span><\/td>\n1,08421<\/span><\/td>\n1,08421<\/span><\/td>\n1,08421<\/span><\/td>\n0,00020<\/span><\/td>\n20<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

La distribuci\u00f3 estad\u00edstica que m\u00e9s s\u2019apropa al moviment de la variaci\u00f3 de preus \u00e9s la <\/span>distribuci\u00f3 normal<\/b>. <\/span> <\/p>\n

La distribuci\u00f3n normal tiene una serie de caracter\u00edsticas que se aprovechan para el c\u00e1lculo cuantitativo de activos financieros dada su aproximaci\u00f3n al movimiento real de \u00e9stos.<\/span><\/p>\n

Lo m\u00e1s claro es la volatilidad.<\/span><\/p>\n

La volatilidad va asociada al concepto de desviaci\u00f3n est\u00e1ndar de una distribuci\u00f3n normal.<\/span><\/p>\n

Nota<\/i><\/b>. Aplicaremos la f\u00f3rmula de la \u201cDesviaci\u00f3n Est\u00e1ndar Muestral\u201d que cambia ligeramente respecto a la de la \u201cDesviaci\u00f3n Est\u00e1ndar Poblacional\u201d. <\/span><\/i><\/p>\n

\"\"<\/p>\n

s <\/b>\u00b7 Desviaci\u00f3n est\u00e1ndard mostral.<\/span><\/p>\n

n <\/b>\u00b7 Tama\u00f1o de la muestra.<\/span><\/p>\n

x<\/span>i<\/span> \u00b7 Observaciones de la muestra.<\/span><\/p>\n

x\u0304 \u00b7 Media de la muestra.<\/span><\/p>\n

Por ejemplo, teniendo en cuenta la muestra horaria de variaciones de precio anterior (en pips) tenemos los siguientes resultados:<\/span><\/p>\n\n\n\n\n\n
n<\/span><\/td>\n 24 <\/span><\/td>\n<\/tr>\n
x\u0304<\/span><\/td>\n 12,71 <\/span><\/td>\n<\/tr>\n
\u2211(x\u1d62 – x\u0304)\u00b2<\/b><\/td>\n 63771,96 <\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Y la desviaci\u00f3n est\u00e1ndar es de: 52,66 pips (0.0005266$).<\/span><\/p>\n

Seg\u00fan la regla emp\u00edrica y de forma aproximada, en una distribuci\u00f3n normal:<\/span><\/p>\n

El 68% de las observaciones se encuentran dentro de una desviaci\u00f3n est\u00e1ndar de la media.<\/span><\/p>\n

El 95% de las observaciones se encuentran en dos desviaciones est\u00e1ndar de la media.<\/span><\/p>\n

El 99.7% de las observaciones se encuentran en tres desviaciones est\u00e1ndar de la media.<\/span><\/p>\n

Ahora imaginamos que nos interesa saber el movimiento del precio del EURUSD en un mes si se mantienen las condiciones actuales.<\/span><\/p>\n

Para trasladar la desviaci\u00f3n t\u00edpica de un per\u00edodo a otro usamos la ra\u00edz del per\u00edodo.<\/span><\/p>\n

Ejemplo, si la variaci\u00f3n horaria que hemos calculado tiene una desviaci\u00f3n de 52,66 pips y queremos calcular la que podr\u00eda tener de forma mensual, multiplicamos por un factor que corresponde a la ra\u00edz cuadrada de las horas que tiene un mes.<\/span><\/p>\n

Suponiendo un mes de 30 d\u00edas y cuatro semanas, sabiendo que el EURUSD habr\u00e1 funcionado los 5 d\u00edas laborables tenemos que un mes tendr\u00e1 (30 – 4*2) * 24 = 528 horas. Por tanto: <\/span><\/p>\n

\"\"<\/p>\n

Por tanto, dentro de uno m\u00e1s la posibilidad de que el EURUSD se mantenga entre los siguientes valores: 1,08421 \u00b1 0,01210 es de 68%.<\/span><\/p>\n

Como vemos, usar la distribuci\u00f3n normal como aproximaci\u00f3n del movimiento de la variaci\u00f3n del precio es muy \u00fatil para realizar suposiciones.<\/span><\/p>\n

Debemos tener en cuenta que he supuesto que la media de las variaciones del precio del EURUSD es igual o muy cercana a cero. Lo que implica que consideremos su movimiento como aleatorio (estoc\u00e1stico). <\/span><\/p>\n

La distribuci\u00f3n Lognormal y la volatilidad<\/b><\/p>\n

Si consideramos que el movimiento de los precios se acerca a una distribuci\u00f3n lognormal (m\u00e1s que a una distribuci\u00f3n normal) podemos deducir que la variaci\u00f3n del logaritmo neperiano de los precios sigue una distribuci\u00f3n normal.<\/span><\/p>\n

Por tanto, si en el apartado anterior partemos de la diferencia de los precios para calcular la desviaci\u00f3n est\u00e1ndar, ahora partiremos de la diferencia de los logaritmos neperianos de los precios para calcular la desviaci\u00f3n est\u00e1ndar.<\/span><\/p>\n

Continuamos con el ejemplo anterior:<\/span><\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Hora<\/b><\/td>\nAsk<\/b><\/td>\nBid<\/b><\/td>\nPrecio<\/b><\/td>\nLn Precio<\/b><\/td>\nVariaci\u00f3n horaria<\/b><\/td>\n<\/tr>\n
1:00:00<\/span><\/td>\n1,08117<\/span><\/td>\n1,08115<\/span><\/td>\n1,08116<\/span><\/td>\n0,07803<\/span><\/td>\n0<\/span><\/td>\n<\/tr>\n
2:00:00<\/span><\/td>\n1,08215<\/span><\/td>\n1,08212<\/span><\/td>\n1,08214<\/span><\/td>\n0,07894<\/span><\/td>\n0,00090<\/span><\/td>\n<\/tr>\n
3:00:00<\/span><\/td>\n1,08187<\/span><\/td>\n1,08184<\/span><\/td>\n1,08186<\/span><\/td>\n0,07868<\/span><\/td>\n-0,00026<\/span><\/td>\n<\/tr>\n
4:00:00<\/span><\/td>\n1,08171<\/span><\/td>\n1,08170<\/span><\/td>\n1,08171<\/span><\/td>\n0,07854<\/span><\/td>\n-0,00014<\/span><\/td>\n<\/tr>\n
5:00:00<\/span><\/td>\n1,08140<\/span><\/td>\n1,08137<\/span><\/td>\n1,08139<\/span><\/td>\n0,07824<\/span><\/td>\n-0,00030<\/span><\/td>\n<\/tr>\n
6:00:00<\/span><\/td>\n1,08124<\/span><\/td>\n1,08122<\/span><\/td>\n1,08123<\/span><\/td>\n0,07810<\/span><\/td>\n-0,00014<\/span><\/td>\n<\/tr>\n
7:00:00<\/span><\/td>\n1,08091<\/span><\/td>\n1,08091<\/span><\/td>\n1,08091<\/span><\/td>\n0,07780<\/span><\/td>\n-0,00030<\/span><\/td>\n<\/tr>\n
8:00:00<\/span><\/td>\n1,08127<\/span><\/td>\n1,08126<\/span><\/td>\n1,08127<\/span><\/td>\n0,07813<\/span><\/td>\n0,00033<\/span><\/td>\n<\/tr>\n
9:00:00<\/span><\/td>\n1,08112<\/span><\/td>\n1,08110<\/span><\/td>\n1,08111<\/span><\/td>\n0,07799<\/span><\/td>\n-0,00014<\/span><\/td>\n<\/tr>\n
10:00:00<\/span><\/td>\n1,08162<\/span><\/td>\n1,08156<\/span><\/td>\n1,08159<\/span><\/td>\n0,07843<\/span><\/td>\n0,00044<\/span><\/td>\n<\/tr>\n
11:00:00<\/span><\/td>\n1,08108<\/span><\/td>\n1,08105<\/span><\/td>\n1,08107<\/span><\/td>\n0,07795<\/span><\/td>\n-0,00049<\/span><\/td>\n<\/tr>\n
12:00:00<\/span><\/td>\n1,08189<\/span><\/td>\n1,08187<\/span><\/td>\n1,08188<\/span><\/td>\n0,07870<\/span><\/td>\n0,00075<\/span><\/td>\n<\/tr>\n
13:00:00<\/span><\/td>\n1,08132<\/span><\/td>\n1,08129<\/span><\/td>\n1,08131<\/span><\/td>\n0,07817<\/span><\/td>\n-0,00053<\/span><\/td>\n<\/tr>\n
14:00:00<\/span><\/td>\n1,08129<\/span><\/td>\n1,08127<\/span><\/td>\n1,08128<\/span><\/td>\n0,07815<\/span><\/td>\n-0,00002<\/span><\/td>\n<\/tr>\n
15:00:00<\/span><\/td>\n1,08221<\/span><\/td>\n1,08199<\/span><\/td>\n1,08210<\/span><\/td>\n0,07890<\/span><\/td>\n0,00076<\/span><\/td>\n<\/tr>\n
16:00:00<\/span><\/td>\n1,08356<\/span><\/td>\n1,08354<\/span><\/td>\n1,08355<\/span><\/td>\n0,08024<\/span><\/td>\n0,00134<\/span><\/td>\n<\/tr>\n
17:00:00<\/span><\/td>\n1,08308<\/span><\/td>\n1,08306<\/span><\/td>\n1,08307<\/span><\/td>\n0,07980<\/span><\/td>\n-0,00044<\/span><\/td>\n<\/tr>\n
18:00:00<\/span><\/td>\n1,08379<\/span><\/td>\n1,08376<\/span><\/td>\n1,08378<\/span><\/td>\n0,08045<\/span><\/td>\n0,00065<\/span><\/td>\n<\/tr>\n
19:00:00<\/span><\/td>\n1,08408<\/span><\/td>\n1,08406<\/span><\/td>\n1,08407<\/span><\/td>\n0,08072<\/span><\/td>\n0,00027<\/span><\/td>\n<\/tr>\n
20:00:00<\/span><\/td>\n1,08415<\/span><\/td>\n1,08412<\/span><\/td>\n1,08414<\/span><\/td>\n0,08078<\/span><\/td>\n0,00006<\/span><\/td>\n<\/tr>\n
21:00:00<\/span><\/td>\n1,08374<\/span><\/td>\n1,08373<\/span><\/td>\n1,08374<\/span><\/td>\n0,08041<\/span><\/td>\n-0,00037<\/span><\/td>\n<\/tr>\n
22:00:00<\/span><\/td>\n1,08408<\/span><\/td>\n1,08372<\/span><\/td>\n1,08390<\/span><\/td>\n0,08057<\/span><\/td>\n0,00015<\/span><\/td>\n<\/tr>\n
23:00:00<\/span><\/td>\n1,08407<\/span><\/td>\n1,08395<\/span><\/td>\n1,08401<\/span><\/td>\n0,08067<\/span><\/td>\n0,00010<\/span><\/td>\n<\/tr>\n
0:00:00<\/span><\/td>\n1,08421<\/span><\/td>\n1,08421<\/span><\/td>\n1,08421<\/span><\/td>\n0,08085<\/span><\/td>\n0,00018<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

La variaci\u00f3n horaria es la observaci\u00f3n muestral que utilizaremos para calcular la desviaci\u00f3n est\u00e1ndar.<\/span><\/p>\n

Un apunte, la variaci\u00f3n horaria la hemos calculado a partir de la variaci\u00f3n del logaritmo neperiano del precio actual y el logaritmo neperiano del precio anterior. Conociendo el c\u00e1lculo de logaritmos podemos deducir que podr\u00edamos haber calculado la variaci\u00f3n haciendo el logaritmo neperiano del precio actual dividido por el precio anterior. Y, lo m\u00e1s importante, el resultado se parecer\u00eda mucho si lo hubi\u00e9semos calculado de la siguiente manera: Diferencia del precio actual y el anterior dividido entre la media del precio actual y el precio anterior. <\/span><\/p>\n

En definitiva, la variaci\u00f3n que hemos calculado no deja de ser una variaci\u00f3n en tanto por uno de los precios (multiplicante por ciento tendr\u00edamos una variaci\u00f3n porcentual del precio).<\/span><\/p>\n

Ahora calculamos su desviaci\u00f3n est\u00e1ndar usando la f\u00f3rmula que ya conocemos:<\/span> \"\"<\/p>\n\n\n\n\n\n\n\n\n
n<\/span><\/td>\n24<\/span><\/td>\n<\/tr>\n
x\u0304<\/span><\/td>\n0,000117378<\/span><\/td>\n<\/tr>\n
\u2211(x\u1d62 – x\u0304)\u00b2<\/b><\/td>\n0,000005445<\/span><\/td>\n<\/tr>\n
<\/td>\n<\/td>\n<\/tr>\n
s horaria<\/span><\/td>\n0,000486555<\/span><\/td>\n<\/tr>\n
s mensual<\/span><\/td>\n0,01118019203<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

La desviaci\u00f3n est\u00e1ndar de esta distribuci\u00f3n expresada en tanto por ciento la conocemos como volatilidad.<\/span><\/p>\n

La desviaci\u00f3n horaria es de 0,000486555 y la mensual (multiplicante por la ra\u00edz de 528) es de 0,01118. Por tanto, y multiplicando por 100, podemos decir que la volatilidad horaria es de 0.05% y la mensual, de 1,12%. <\/span><\/p>\n

En definitiva, existe un 68% de posibilidades de que el precio de la EURUSD se haya movido dentro del margen de \u00b11,12% a finales de este mes.<\/span><\/p>\n

Hay un 95% de posibilidades de que el precio de EURUSD se haya movido dentro del margen de \u00b12,24% a finales de este mes.<\/span><\/p>\n

Hay un 99,7% de posibilidades de que el precio de la EURUSD se haya movido dentro del margen de \u00b13,36% a finales de este mes.<\/span><\/p>\n

Cuando nos hablan de que EURUSD tiene una volatilidad anual de 4% podemos hacer el ejercicio inverso al que hemos hecho hasta ahora y averiguar qu\u00e9 volatilidad mensual ser\u00eda:<\/span><\/p>\n

Volatilidad anual = 4%<\/span><\/p>\n

Volatilidad mensual = Volatilidad anual \/ SQR(12) = 1,15%<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Para explicar este apartado partiremos de un caso pr\u00e1ctico: Cogemos como ejemplo el movimiento del EURUSD y elegimos como per\u00edodo de c\u00e1lculo el de una hora. Debemos tener en cuenta que podr\u00edamos haber cogido cualquier per\u00edodo para hacer el ejemplo (un minuto, 5 minutos, una semana, etc.). Cogemos como precio la media entre el precio […]<\/p>\n","protected":false},"author":1,"featured_media":25048,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[19],"tags":[],"class_list":["post-25206","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-didactico"],"_links":{"self":[{"href":"https:\/\/qooant.com\/es\/wp-json\/wp\/v2\/posts\/25206","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/qooant.com\/es\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/qooant.com\/es\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/qooant.com\/es\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/qooant.com\/es\/wp-json\/wp\/v2\/comments?post=25206"}],"version-history":[{"count":1,"href":"https:\/\/qooant.com\/es\/wp-json\/wp\/v2\/posts\/25206\/revisions"}],"predecessor-version":[{"id":25207,"href":"https:\/\/qooant.com\/es\/wp-json\/wp\/v2\/posts\/25206\/revisions\/25207"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/qooant.com\/es\/wp-json\/wp\/v2\/media\/25048"}],"wp:attachment":[{"href":"https:\/\/qooant.com\/es\/wp-json\/wp\/v2\/media?parent=25206"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/qooant.com\/es\/wp-json\/wp\/v2\/categories?post=25206"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/qooant.com\/es\/wp-json\/wp\/v2\/tags?post=25206"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}