In this article we propose a method of parameters estimation for the class of discrete stable laws. Discrete stable distributions form a discrete analogy to classical stable distributions and share many interesting properties with them such as heavy tails and skewness. Similarly as stable laws discrete stable distributions are defined through characteristic function and do not posses a probability mass function in closed form. This inhibits the use of classical estimation methods such as maximum likelihood and other approach has to be applied. We depart from the H-method of maximum likelihood suggested by Kagan (1976) where the likelihood function is replaced by a function called informant which is an approximation of the likelihood function in some Hilbert space. For this method only some functionals of the distribution are required, such as probability generating function or characteristic function. We adopt this method for the case of discrete stable distributions and in a simulation study show the performance of this method.
Daniel (32 let), v anamnéze dlouhodobé užívání kombinací návykových látek, nejčastěji marihuany, pervitinu, heroinu a alkoholu. Návykové látky začal užívat zhruba od 15 let z důvodu pozitivní rodinné anamnézy, vztahových a osobnostních problémů. Psychoterapeuticky jsme spolu pracovali během jeho tříměsíční toxirehabilitační léčby v Psychiatrické nemocnici v Kroměříži. Jméno pacienta bylo v kazuistice změněno. Daniel spolu s dalšími spolupacienty se podíleli na vytvoření programu a následně brožury pro pacienty s drogovou kariérou s kognitivně behaviorálními terapeutickými postupy. V terapeutickém cíli Daniela dominují témata bažení, jeho osobnostní nastavení, učení se sebeovládání: odmítání drogy, komunikace, práce se vztekem, nácvik relaxace, kognitivní vyhýbání se návykové látce, řešení problémů, prevence relapsu. and Daniel (32 years old), with an anamnesis of long-term using of addictive substances, more precisely a combination of marihuana, methamphetamine, heroin and alcohol. He started taking addictive substances approximately at the age of 15 because of a positive family anamnesis, relationship and personal problems. From the psychotherapist’s perspective we worked together during his tree-month toxin-rehabilitation treatment in the psychiatric hospital in Kromeriz. The patient's name has been changed in case history. Daniel, together with other patients contributed to the creation of a programme and afterwards a brochure for patients with drugs career, based on cognitive – behavioural therapist techniques. Daniel's therapeutic goals are dominated by craving themes, his personality settings, learning self-control: drug rejection, communication, work with rage, relaxation training, cognitive avoidance with addictive substance, problem solving, and relapse prevention.