{"id":18657,"date":"2022-11-01T13:43:35","date_gmt":"2022-11-01T08:13:35","guid":{"rendered":"https:\/\/jassweb.com\/solved\/solved-how-to-create-4-random-defined-percentages-that-sum-1\/"},"modified":"2022-11-01T13:43:35","modified_gmt":"2022-11-01T08:13:35","slug":"solved-how-to-create-4-random-defined-percentages-that-sum-1","status":"publish","type":"post","link":"https:\/\/jassweb.com\/solved\/solved-how-to-create-4-random-defined-percentages-that-sum-1\/","title":{"rendered":"[Solved] How to create 4 random defined percentages that sum 1"},"content":{"rendered":"<p> [ad_1]<br \/>\n<\/p>\n<div id=\"answer-54675935\" class=\"answer js-answer accepted-answer js-accepted-answer\" data-answerid=\"54675935\" data-parentid=\"54675701\" data-score=\"3\" data-position-on-page=\"1\" data-highest-scored=\"1\" data-question-has-accepted-highest-score=\"1\" itemprop=\"acceptedAnswer\" itemscope itemtype=\"https:\/\/schema.org\/Answer\">\n<div class=\"post-layout\">\n<div class=\"votecell post-layout--left\"><\/div>\n<div class=\"answercell post-layout--right\">\n<div class=\"s-prose js-post-body\" itemprop=\"text\">\n<p>Let<\/p>\n<pre><code>ll &lt;- c(0.2, 0.2, 0.15, 0.15)\nul &lt;- c(0.5, 0.5, 0.4, 0.3)\n<\/code><\/pre>\n<p>where <code>ll<\/code> and <code>ul<\/code> correspond to lower and upper limits for each of the random variables. Next,<\/p>\n<pre><code>x &lt;- runif(length(ll), 0, ul - ll)\n<\/code><\/pre>\n<p>is a vector of uniform random draws from intervals [0,0.3], [0,0.3], [0,0.25], and [0,0.15]. The reason for this is that our final vector is<\/p>\n<pre><code>if(sum(x) &gt; 1 - sum(ll)) {\n  ll + x \/ sum(x) * (1 - sum(ll))\n} else {\n  ll + x + (ul - ll - x) \/ sum(ul - ll - x) * (1 - sum(x) - sum(ll))\n}\n# [1] 0.3112532 0.2927185 0.2347163 0.1613119\n<\/code><\/pre>\n<p>So, if <code>sum(x) &gt; 1 - sum(ll)<\/code>, this means that <code>x<\/code> is too large. In that case we renormalize it by making it smaller. In this way all the constraints are satisfied. Otherwise, <code>x<\/code> is too small. In that case we are going to add a portion of <code>ul - ll - x<\/code>. Now the key is that necessarily<\/p>\n<pre><code>sum(ul - ll - x) &gt; (1 - sum(x) - sum(ll))\n<\/code><\/pre>\n<p>which means that <code>ul - ll - x<\/code> doesn&#8217;t get increased and, hence, again all the restrictions are satisfied.<\/p>\n<p>Kernel densities of the respective elements are as follows<\/p>\n<p><a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/jassweb.com\/solved\/wp-content\/uploads\/2022\/11\/Solved-How-to-create-4-random-defined-percentages-that-sum.png\"><img decoding=\"async\" src=\"https:\/\/jassweb.com\/solved\/wp-content\/uploads\/2022\/11\/Solved-How-to-create-4-random-defined-percentages-that-sum.png\" alt=\"enter image description here\"><\/a><\/p>\n<\/p><\/div>\n<div class=\"mt24\"><\/div>\n<\/div>\n<p>            <span class=\"d-none\" itemprop=\"commentCount\"><\/span> <\/p><\/div>\n<\/div>\n<p>[ad_2]<\/p>\n<p>solved How to create 4 random defined percentages that sum 1 <\/p>\n","protected":false},"excerpt":{"rendered":"<p>[ad_1] Let ll &lt;- c(0.2, 0.2, 0.15, 0.15) ul &lt;- c(0.5, 0.5, 0.4, 0.3) where ll and ul correspond to lower and upper limits for each of the random variables. Next, x &lt;- runif(length(ll), 0, ul &#8211; ll) is a vector of uniform random draws from intervals [0,0.3], [0,0.3], [0,0.25], and [0,0.15]. The reason for &#8230; <a title=\"[Solved] How to create 4 random defined percentages that sum 1\" class=\"read-more\" href=\"https:\/\/jassweb.com\/solved\/solved-how-to-create-4-random-defined-percentages-that-sum-1\/\" aria-label=\"More on [Solved] How to create 4 random defined percentages that sum 1\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[320],"tags":[321],"class_list":["post-18657","post","type-post","status-publish","format-standard","hentry","category-solved","tag-r"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>[Solved] How to create 4 random defined percentages that sum 1 - JassWeb<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/jassweb.com\/solved\/solved-how-to-create-4-random-defined-percentages-that-sum-1\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"[Solved] How to create 4 random defined percentages that sum 1 - JassWeb\" \/>\n<meta property=\"og:description\" content=\"[ad_1] Let ll &lt;- c(0.2, 0.2, 0.15, 0.15) ul &lt;- c(0.5, 0.5, 0.4, 0.3) where ll and ul correspond to lower and upper limits for each of the random variables. Next, x &lt;- runif(length(ll), 0, ul - ll) is a vector of uniform random draws from intervals [0,0.3], [0,0.3], [0,0.25], and [0,0.15]. The reason for ... 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