Estimation of the Mean and Standard Deviation of the Logistic Distribution Based on Multiply Type-II Censored Samples

In this paper, we discuss the problem of estimating the mean and standard deviation of a logistic population based on multiply Type-II censored samples. First, we discuss the best linear unbiased estimation and the maximum likelihood estimation methods. Next, by appropriately approximating the likelihood equations we derive approximate maximum likelihood estimators for the two parameters and show that these estimators are quite useful as they do not need the construction of any special tables (as required for the best linear unbiased estimators) and are explicit estimators (unlike the maximum likelihood estimators which need to be determined by numerical methods). We show that these estimators are also quite efficient, and derive the asymptotic variances and covariance of the estimators. Finally, we present an example to illustrate the methods of estimation discussed in this paper.     

Multivariate Generalized Distributions of Order k

Abstract

The study of multivariate distributions of order k, two of which are the multivariate negative binomial of order k and the multinomial of the same order, was introduced in Philippou et al. (Philippou, A. N., Antzoulakos, D. L., Tripsiannis, G. A. (1988 Philippou, A. N., Antzoulakos, D. L. and Tripsiannis, G. A. 1988. Multivariate distributions of order k. Statistics and Probability Letters, 7(3): 207–216.  [Google Scholar]). Multivariate distributions of order k. Statistics and Probability Letters 7(3):207–216.), and Philippou et al. (Philippou, A. N., Antzoulakos, D. L., Tripsiannis, G. A. (1990 Philippou, A. N., Antzoulakos, D. L. and Tripsiannis, G. A. 1990. Multivariate distributions of order k, part II. Statistics and Probability Letters, 10(1): 29–35.  [Google Scholar]). Multivariate distributions of order k, part II. Statistics and Probability Letters 10(1):29–35.). Recently, an order k (or cluster) generalized negative binomial distribution and a multivariate negative binomial distribution were derived in Sen and Jain (Sen, K., Jain, R. (1996 Sen, K. and Jain, R. 1996. “Cluster generalized negative binomial distribution”. In Probability Models and Statistics Medhi Festschrift, A. J., on the Occasion of his 70th Birthday Edited by: Borthakur, A. C. 227–241. New Delhi: New Age International Publishers.  [Google Scholar]). Cluster generalized negative binomial distribution. In: Borthakur et al. A. C., Eds.; Probability Models and Statistics Medhi Festschrift, A. J., on the Occasion of his 70th Birthday. New Age International Publishers: New Delhi, 227–241.) and Sen and Jain (Sen, K., Jain, R. (1997 Sen, K. and Jain, R. 1997. A multivariate generalized Polya-Eggenberger probability model-first passage approach. Communications in Statistics—Theory and Methods, 26: 871–884. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). A multivariate generalized Polya-Eggenberger probability model-first passage approach. Communications in Statistics-Theory and Methods 26:871–884.), respectively. In this paper, all four distributions are generalized to a multivariate generalized negative binomial distribution of order k by means of an appropriate sampling scheme and a first passage event. This new distribution includes as special cases several known and new multivariate distributions of order k, and gives rise in the limit to multivariate generalized logarithmic, Poisson and Borel-Tanner distributions of the same order. Applications are indicated.     

Acquisition as a means for external technology sourcing: Complementary, substitutive or both?

This paper addresses the question of how a target firm's innovation activities relate to the acquiring firm's R&D characteristics, and more specifically, if the former substitute for, or complement the acquirer's activities. It investigates this question in three narrowly defined high technology industries by analysing the association of three R&D characteristics of acquiring firms with different measures of acquisition extent and content. The R&D characteristics referred to are: addressing R&D efforts, R&D outputs and absorptive capacity. Data was collected in each case for those firms whose combined sales revenue makes up 80% of the industry total and is used to test a set of hypotheses derived from extant literature. The findings confirm a substitutive relationship between acquisitions and acquirer research efforts as well as between acquirer and target patent output, whereas absorptive capacity is complementary to acquisition activities. The results reveal that acquirers target firms that hold a large number of patents in the fields where acquirer patenting is weak, and so address weaknesses in their own R&D output. This finding extends the extant literature on the role of external technology sourcing in the high technology context. Research findings are presented along with their implications and directions for future research.     

From stagnation to growth: Revisiting three historical regimes

This paper explores the role of mortality in the long transition from Malthusian stagnation to sustained economic growth. An endogenous child mortality rate that varies inversely with parents standard of living is added to the framework in Galor and Weil (AER 2000). In our version of the model, the transition from stagnation to growth, triggered by an exogenous shock to technology, comprises a mortality revolution succeeded by a demographic transition.This paper has benefitted from discussions with and suggestions made by KarlGunnar Persson, Christian Schultz, and, particularly, Christian Groth at the University of Copenhagen. I gratefully acknowledge the insightful criticisms of two anonymous referees, and I thank Paula Madsen for English proof-reading. Responsible editor: Alessandro Cigno.     

Malthus in state space: Macro economic-demographic relations in English history, 1540 to 1870

. The history of preindustrial Europe provides an opportunity to examine the causes and consequences of population change at a macro level. However, serious statistical problems arise from the endogeneity of all observed variables in a Malthusian system (fertility, mortality, population size, and real wages), and from unobserved influences such as shifts in the demand for labor and variations in health. These problems have undermined both informal inference from the data and more complex econometric investigations. This paper takes a new statistical approach, finding the maximum likelihood estimate of a state space representation of the Malthusian system by repeated application of Kalman filter methods, using annual data from England, 1540 to 1870. The new estimates confirm some findings of the earlier literature and contradict others. Some variables are estimated for the first time. Implications are discussed for the interpretation of English economic-demographic history. Received: 3 January 2000/Accepted: 22 January 2001     

The ageing of society, health services provision and taxes

This paper investigates the outcome of ageing on taxes and hospitalisation of the elderly using panel data on 23 Swedish county councils 1980–1999. We test two hypotheses; whether a larger share of elderly has no negative effect on bed days per elderly person and no positive effect on tax rates. We reject the first hypothesis but fail to reject the second hypothesis. Further we cannot reject the hypothesis of a unitary elasticity of the share of elderly on bed days per elderly person. These results imply that the old bear the entire cost of adjustment when the population grows older.     

Social trust and human development

A series of studies connect social trust to economic growth. In this paper, we explore the connection between trust and a broader measure of development, the UN Human Development Index. We find that trust is significantly associated with faster human development in the 1980–2005 period. The impact of trust occurs mainly in less democratic countries.     

Optimal food allocation in a slave economy

We propose a model of food allocation in an economy in which property rights exist in human beings. We assume that a slave-owner allocates food over the slave's lifetime so as to maximise his own wealth. The slave's productive capacity is determined endogenously by food consumption. Food allotment during childhood and adolescence determines productive capacity over the life course. The slave owner chooses optimal time paths of food allotment in light of the contribution food makes to both the level and growth of physical capacity, as a function of the price of food and of the value of the slave's productivity. Though conceived for an economy in which property rights exist in human beings, the model can be modified so as to apply to resource allocation within a household economy in which parents provide both nourishment and schooling for their children, in order to enhance their current or future productivity. Received: 14 April 2000/Accepted: 25 August 2001     

5-(4-羟基苯基)-10,15,20-三苯基卟啉在醋酸中电子吸收光谱研究

研究了 5- (4-羟基苯基 ) - 1 0 ,1 5 ,2 0 -三苯基卟啉 (H2 L)在醋酸中电子吸收光谱 结果表明 ,5- (4-羟基苯基 ) - 1 0 ,1 5,2 0 -三苯基卟啉在冰醋酸中以二酸形式H4L2 和游离碱H2 L形式存在 ,二者之间存在着电离平衡 :H4L2 =H2 L 2H