Moment relations for some discrete distributions

Summary

Recursion relations for moments not involving differentiation with respect to the parameter of the distribution are given for the Poisson distribution in Philipson (1963) and those for the logarithmic series distribution in Patil, Kamat and Wani (1964) and Patil and Wani (1965). Similar results are obtained here for the negative binomial distribution. The relations referred to above are obtained as corollaries.     

On the asymptotic normality of some unbiased estimates

Abstract

Let X _m(n) =(X _j , n, ..., X _{j m,n} ) be a subset of observations of a sample X_n = (X_1n X _2n ... , X _nn ). Here the X_jn 'S in Xn are not necessarily independent or identically distributed, and m(n) mayor may not tend to infinity as n tends to infinity. Suppose the joint density function h_n =h_n (x _m (n); θ) of the X _jn 's in Xm(n) is completely specified except the values of the parameters in the parameter vector θ = (θ1 θ2, ... , θ _k ), where θ belongs to a non-degenerate open subset H of the k-dimensional Euclidean space Rk and k?m(n).     

A note on the consistency of maximum likelihood estimators

Abstract

A sequence of maximum likelihood estimators based on a sequence of independent but not necessarily identically distributed random variables is shown to be consistent under certain assumptions. Some examples are given to show that these assumptions are easy to verify and not very restrictive.     

Consistency and asymptotic normality of maximum likelyhood estimators

Abstract

Let the random variable X denote the time taken in completion of a process. For a fixed a, if the observed value of X is less than a, the X is observable, but if X is greater than a, the process is tampered with and is accelerated or decelerated at time a by some unknown factor α, and Y=a+α(X-a) is observed. If the experimenter has only partial control over the experiment, it may be difficult to get several observations on Y corresponding to the same a value. Thus we have a set of independent but not identically distributed observations. The large sample behavior of m.l.e. of the unknown parameters based on tampered random variables Y ^b1 , ..., Y ^bn is studied. If X follows an exponential distribution with mean (1/--), ... the consistency and asymptotic normality of the m.l.e. of α and -- is established under mild conditions on a ^b1, a ^b2, ... The conditions needed for establishing the consistency of m.l.e. of lX are given when X follows a uniform distribution U(O, --) or when X has any known distributional form     

The Impact of Search Costs and Asymmetric Information on Current Value Accounting

This paper examines the impact that search costs and asymmetric information would have on financial statements if either of the two main systems of current value accounting were introduced. The significance of search costs is that, although the models which determine the optimal amount of search are becoming more general, they are based on very restrictive assumptions and are of limited practical application. In relation to the second issue, where asset markets are dominated by asymmetric information, the ‘signal’ conveyed by the accounts would be misleading. It is argued that, whilst these two issues can more easily be resolved where the provision of financial information is unregulated, they are likely to be important considerations in the political process which results in an accounting standard.     

Initial Public Offerings on the Unlisted Securities Market: The Impact of Professional Advisers

This paper tests two hypotheses developed in the context of information asymmetry between companies making initial public offerings (IPO) on the Unlisted Securities Market and potential investors. It is argued that the status of the sponsor and audit firm are interpreted by potential investors as signals of an IPO's quality. The results indicate that for IPOs made during 1986–87 the level of discount and the status of the associated auditing firm are significantly related. Higher quality auditing firms are associated with lower levels of discount. A similar relationship for IPOs made during the period 1988–89 is not detected. The paper suggests that there were significant changes in the IPO market between these two periods. No relationship in either period is detected between the level of discount and the status of the sponsor.