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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARYThe Hermite distribution is the generalized Poisson distribution whose probability generating function (P.G.F.) is exp [a1(s -1) + a2(s2 -1)]. The probabilities (and factorial moments) can be conveniently expressed in terms of modified Hermite polynomials (hence the proposed name). Writing these in confluent hypergeometric form leads to two quite different representations of any particular probability-one a finite series, the other an infinite series.The cumulants and moments are given. Necessary conditions on the parameters and their maximum-likelihood estimation are discussed.It is shown, with examples, that the Hermite distribution is a special case of the Poisson Binomial distribution (n = 2) and may be regarded as either the distribution of the sum of two correlated Poisson variables or the distribution of the sum of an ordinary Poisson variable and an (independent) Poisson 'doublet' variable (i.e. the occurrence of pairs of events is distributed as a Poisson).Lastly its use as a penultimate limiting form of distributions with P.G.F. exp a (si-1)is examined.

Summary A one‐line algorithm LB is given for generating samples from the logarithmic series distribution. Two independent uniform random variables are converted into a single logarithmic variable by use of a structural property of the distribution. Faster versions of the method, algorithms LBM and LK, employ simple initial tests which identify those pairs of uniform random variables which yield the most frequently occurring values of the logarithmic variable. Comparison with a search method, algorithm LS, shows that the search method is faster when the parameter a of the logarithmic distribution is less than about 0‐95. However, values of a greater than 095 are often encountered. In ecological contexts a ranges from 0‐9 to 0‐9999; here the search method becomes prohibitively slow, and the algorithms based on the structural method are preferable. Both methods lead to very short, portable, procedures which require a trivial amount of storage.

2. Three experiments with mature dry Friesian cows lasted for up to 16 days. Nitrate was given as nitrate-rich hay or mixed with concentrates to supply from 2.4 to 16.0 g/100 kg liveweight at each meal. To test the hypothesis that methaemoglobin was formed as the result of the production of nitrite as an intermediate in the rumen, one group was given a daily supplement of KNO2, 2 to 3 g/100 kg liveweight. Blood was sampled at frequent intervals, and ruminal fluid was sampled every 15 min for short periods from cows with a recirculating sampling device. Large intakes of nitrate in either form increased nitrite in the rumen, leading to increase of methaemoglobin in the blood during the first few days, after which the high value was maintained. The high methaemoglobin value was positively correlated with the larger nitrite content in the rumen. Results are discussed in the light of conflicting reports on the tolerance of cattle to large amounts of nitrate and the importance of frequent sampling to obtain a true picture is stressed. Previous inferences regarding the ability of cattle to tolerate nitrate at up to 90 g/100 kg are considered to be mistaken. ADDITIONAL ABSTRACT: In two experiments groups of 4 cows (415-669 kg body weight) received similar daily amounts of NO3- as either a single oral dose of KNO3 (15 g/100 kg) or a single feed of nitrate rich hay (12.4-15.4 g NO3-/100 kg) for 18 days. In a third experiment 6 cows received 2 or 3 g/100 kg of NO3- as a single oral dose of KNO2 for 6 days. Nitrate, nitrite and ammonia were measured in rumen sample and haemoglobin and methaemoglobin were measured in blood. The daily supply of equal doses of nitrate to cows, as hay with a high nitrate content or as potassium nitrate, induced higher nitrite contents in the rumen fluid and a higher percentage of methaemoglobin in the blood during the first days, after which they remained on this higher level. These increases were probably due to a change in the activity of the reducing micro-organisms in the rumen. The changes also partly explain the controversial data in the literature on the acceptable dosages of nitrate to be supplied to ruminants. This may have led to the mis-interpretation that ruminants should tolerate daily intakes up to 90 g of NO3- per 100 g body weight. (Abstract retrieved from CAB Abstracts by CABI’s permission)