In a duration analysis of enterprises, as a rule there are determined four basic functions related to the time of their duration, i.e.: the density function; the distribution function; the survival function, and the hazard function. It turns out that the hazard function and its cumulative version are the key to understanding modern survival analysis. The aim of the paper is to indicate the best method of the estimation of the values of individual functions in survival analysis based on other functions. The paper provides compiled and classified information on particular functions used in the non-parametric duration analysis of enterprises. It examines some theoretical and practical problems related to the determination of, among others, the hazard function and the cumulative hazard function on the basis of data in cohort tables and the results of the estimation of the survival function with the use of the Kaplan-Meier method. The considerations included in the paper are illustrated with the results of analyses for enterprises established in the Łódzkie Voivodeship in 2001-2015 (including those which went into liquidation).
Can economic stress affect secondary sex ratio in Poland?
The ratio of male to female births described as the male proportion is expected to be about 1.06. The secondary sex ratio can be influenced by various stresses experienced by parents (e.g., parents' exposure to chemical and physical pollution, natural phenomena, wars and economic crises). The seminal study in this field speculated that fewer goods and services than needed or desired might sufficiently stress human populations to lower the secondary sex ratio. The main purpose of this study is to examine the relationship between economic stress and the fluctuations of sex ratio at birth in Poland. The statistical analysis was based on annual demographic data obtained from year-books issued by the Central Statistical Office on the overall number of male and female live births in Poland in the years 1956-2005 as well as on the annual data of percentage change in total private consumption. In order to verify the hypothesis that the observed time-series of the secondary sex ratio in Poland declines with deterioration in economic conditions, we constructed mathematical models (ARIMA) of both analyzed phenomena following the statistical procedure proposed by Catalano and Bruckner . We found a statistically significant decline of SSR in Poland over the last 50 years. The decrease appeared to be stronger in villages than in towns. However, the consumption rate as related to the strength of economic stress had no effect on the fluctuation of the sex ratio at birth.
The article presents the results of the duration analysis for 21,163 enterprises (natural persons conducting economic activity) established in the Łódzkie Voivodship in 2010 and observed until December 31, 2015. The Kaplan-Meier estimation of the survival function, the Cox proportionalhazards model and the recursive partitioning method (the CTree algorithm) are applied to achieve the goal of the conducted research i.e. to answer the following question: does the type of business activity and location of the enterprise affect its duration? Prediction error curves based on the bootstrap crossvalidation estimates of the prediction error are used to assess and compare predictions obtained from all three models. On the basis of the analysis results it can be assumed that the type of business activity makes firms more varied due to their duration compared to their location.