The lower extreme asymptotic is analised in this master’s work. I have analysed the marginal term case, when sample size N is accidental. The ordinary accidental sample is taken from general set, what is spreaded along logistic low. I have searched for logistic dimensions minimum limiting distribution function in the investigative part. Than I’ve practised transfering theorem. My task is to find such normalization, along what logistic dimensions lower extreme distribution functions are geometrically ministable or asymptotically k-stable. I have proved in my job, that first lower extreme distribution function is geometrically ministable, and other distribution functions – asymptotically k-stable.