Geostatistical Ore Reserve Estimation by Michel David

By Michel David

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The mineralized particles are n o w distributed at random in the pulp. Their distribution is thus a Poisson distribution. N o w if w e pick up from each heap of pulp a subsample t o be sent t o the lab and p l o t t h e histo­ gram of the results, w e p l o t in fact the distribution of a random variable which follows a Poisson distribution, the parameter of which itself follows a gamma distribution. One can s h o w that the resulting distribution is the negative binomial. Thus, as the above process describes the usual sampling procedure, w e should e x p e c t almost any sampling distribution t o be a nega­ tive binomial, if grades are expressed in proper units (number of grains rather than %).

5 The negative binomial distribution This is another interesting distribution since it can be generated b y a variety of processes (Johnson and K o t z , 1 9 6 9 ) . 1 . 3 . 5 . 15) Its mean value is equal t o NP and its variance is equal t o NPQ =NP(1 The shape can be seen in Fig. 2 2 . + P). 2 Estimation of parameters and model fitting There is n o simple w a y t o obtain " g o o d " estimators of N and P. A n iterative process is n e e d e d t o obtain the m o s t probable values of these t w o parameters.

OvOsor-r-r~(»ooooooavos — — — r- ii ,e l' «r> «r>ir>ir>tr>ir>»r>\0>CsOvCsCr-i^r-r>ooooooooaN II <* l! i' *N > 22 It can be interpreted as the probability of obtaining draws with replacement, from a p o p u l a t i o n where black portion p. The mean of the distribution is np and the variance is assume a variety of shapes w h i c h might be seen in Fig. fact is that as n tends t o infinity, x tends t o normality (x — np)/y/np^(l — p ) b e c o m e s a unit normal variable. k black balls in n balls are in a pro­ np ( 1 — p ) .

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