PROPERTIES OF THE MAXIMUM LIKELIHOOD ESTIMATES OF THE EXPONENT OF PARETO DISTRIBUTION

This paper investigates the statistical properties of maximum likelihood estimation index of the Pareto distribution. In recent years, power distribution laws such as Pareto distribution attract the attention of researchers in various fields of science and technology, from economics and linguistics to Internet traffic analysis. Therefore, the problem of determining the exponent of the power law for a given sample is of exceptional practical importance. It is analytically proved that this estimate is biased, although valid. A formula that eliminates the bias is proposed. Besides, a formula for the variance of the unbiased estimate is analytically derived. In addition, the problem of finding the distribution function and probability density of this estimate as a random variable is set and analytically solved. Next, a formula for mathematical expectation and dispersion based on previously determined probability density is found. The obtained results can be used in various fields of human activity, for example, to predict the intensity of natural and man-made disasters

Ecological and phytopathological status of birch stands on the territory of Krasnoyarsk group of districts

According to inspection data, the health and vital status of birch (Betula pendula Roth.) stands in Krasnoyarsk group of lands (southern part of Central Siberia) were estimated (established) as satisfactory in general; about half of birch stands near urbanized areas were weakened. The condition of stands decreased significantly with increased recreation use, the effect of technogenic pollution was negligible. The most valuable (important) representatives of pathogenic biota identified on birch trees were infestations of necrotic cancer and rot diseases. In birch stands the bacterial dropsy was found to be widespread (agent of infection – Erwinia multivora Scz.-Parf), occurrence of the disease ranged from a single ill tree up to 10–38 % of the stands. The birch stands in taiga areas were affected to a greater extent than in forest-steppe; there were high yield class stands on moist soils. Prevalence of bacteriosis rose with increasing stand age and density and not dependent on recreation use level. Trees with dropsy are dead in fact or potentially. In taiga birch forests the infection and rot of roots was caused by honey agaric (Armillaria mellea sensu lato), that lead to single or, rarely, group tree drying and the fungus usually eliminated already weakened trees. Wood biomass was destroyed by complex of aphyllophorous Hymenomycetes, their hemiparasitic species caused stem rots that decreased stand marketability and also resulted in rot-realated wind-break accumulation. Occurrence of rot was significantly higher in second growth birch stands, possibly above 20 %; the relationship between rot prevalence and forest assessment was not revealed

SPINAL CORD STIMULATION IN TREATMENT OF THE NEUROPATHIC PAIN SYNDROMES: INITIAL EXPERIENCE

In the article initial experience of spinal cord stimulation for chronic pain syndromes is described. The trial was done for 62 patients, in 52 cases trial was successful and subcutaneous pulse generator were implanated. Maximal follow-up is 26 months. The level of pain evaluates at VAS. Permanent pain-relieve results were achieved in 46 patients (74,2%). These results correspond to literature data