# Random Property

The random distribution, for Density, Poisson, Shear Modulus and Damping, can be:

• Normal distribution: (or Gaussian), is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean
• Uniform distribution: is a probability distribution where all outcomes are equally likely

There are many types of spatial variability, but all refer to the following formula: where:

• XRND = random parameter to be used in the calculation
• μ = average value
• σ = standard deviation capable of disturbing the distribution and ε is the random variable with zero average and one for the standard deviation.

The algorithm proposed by Box and Muller generates the Gaussian distribution (Box, G. E. P.; Muller, Mervin E. A Note on the Generation of Random Normal Deviates. Ann. Math. Statist. 29 (1958) where:

• ε1 and ε2 are two non-correlated (pseudo) random variables with zero mean and unit standard deviation.

The parameter according to numerical value of XRND it is into the range is calculated: For each parameter, the average value and the range of variation (Minimum and Maximum value) is defined. It is possible to use a percentage of variation both minimum and maximum value are automatically calculated as ± (%) on average value.
{"ft_lang_label":"__label__en","ft_lang_prob":0.8977477,"math_prob":0.99316084,"size":1330,"snap":"2022-40-2023-06","text_gpt3_token_len":280,"char_repetition_ratio":0.13951735,"word_repetition_ratio":0.0,"special_character_ratio":0.21052632,"punctuation_ratio":0.125,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9994431,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12],"im_url_duplicate_count":[null,null,null,1,null,1,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-09-30T02:08:49Z\",\"WARC-Record-ID\":\"<urn:uuid:fac43e6c-5446-41bb-8b6d-d6847af291d6>\",\"Content-Length\":\"14218\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:35a4e64c-2be1-4731-910b-fa529164c8fc>\",\"WARC-Concurrent-To\":\"<urn:uuid:f50d0bad-206b-4f7c-b29c-226bc66c0d24>\",\"WARC-IP-Address\":\"5.134.122.201\",\"WARC-Target-URI\":\"http://visualq4m.com/pages/RandomProperty.html\",\"WARC-Payload-Digest\":\"sha1:E37CYWS3VTGJ74CMJH2B35YIRRKNDQIV\",\"WARC-Block-Digest\":\"sha1:IAXHTYA5JZCHC6LC6EKOG3QJSJWDUCTL\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030335424.32_warc_CC-MAIN-20220930020521-20220930050521-00499.warc.gz\"}"}