Methods of estimating the mean duration of enterprises and the mean additional duration of enterprises in Lodzkie Voivodship

Abstract

In a duration analysis, the time of enterprises functioning, i.e. from the foundation to their liquidation, is represented by a random variable. The basic characteristic functions used for time description include: density function, distribution function, survival function and hazard function. The first one f(t) defines the probability of enterprise liquidation in the period denoted as t, i.e. in ⟨t, t + 1) period of time; the second one F(t) expresses the probability of enterprise persistence from the moment of its establishment to the maximum end of the period denoted as t, end of ⟨0, t) period of time; the third one S(t) defines the probability of enterprise survival for longer than the end of the period denoted as t, end of ⟨0, t) period of time; and the last one h(t) assesses the intensity of the process of enterprise liquidation in the period denoted as t. The article presents theoretical and practical aspects of determining selected distribution parameters of time duration: the mean duration of enterprises and the mean additional duration of enterprises, which are also used for characterizing patterns of companies’ survival. The considerations are supported by calculations of the above-mentioned measures for subsequent cohorts of established enterprises (including the liquidated ones) in Lodzkie Voivodship in the years 2001-2015.