Exact moments of order statistics from a power-function distribution

Summary

In this note a problem on exact moments of order statistics from a power-function distribution is considered. The characteristic function of the kth order statistic is obtained and moments about the origin of the kth order statistic are expressed in terms of gamma functions. An exact expression for the covariance of any two order statistics Y_i < Y_j is obtained in terms of beta and gamma functions. Various recurrence relations between the expected values of order statistics are also obtained.     

On moments of order statistics from the pareto distribution

Abstract

The evaluation of multiple integrals which occur in order statistics distribution theory is involved due to the fact that the integration is to be carried on over an ordered range of variables of integration. This difficulty is sometimes completely obviated by transforming the ordered variates to the unordered ones. Several such transformations are available in the Theory of Multiple Integrals. In previous papers [2, 3] the author used one such transformation, and gave alternative simplified proofs of several known results in the distribution theory of order statistics from the exponential and the power function distributions. In this paper we use such a known transformation to derive moments (and distributions if necessary) of order statistics from the Pareto distribution. Malik [4] has derived moments of order statistics from this distribution without the transformation of the ordered variates to the unordered ones. The process of direct integration used by Malik becomes complicated for dealing with the moments of more than two ordered variates. Further, the method which we use here is unformly applicable to derive the moments or the distributions of one or more ordered variables, and gives the distributions and moments without any complicated steps in integration. The transformation used by us considerably simplifies the manipulations necessary for the derivation of moments or the Mellin transforms, and thus we hope that our paper would at least be of Pedagogical interest.     

Inverse moments of order statistics from Weibull distribution

Abstract

A general expression for moments of order statistics of positive and negative orders from Weibull distribution has been obtained and the result has been utilized to establish two identities.     

The distributions of the first and second order moments,the partial correlation coefficients and the multiple correlation coefficient in samples from a normal multivariate population

Abstract

1. When the frequency function of a statistical variable is known, one of the most important tasks of Theoretical Statistics is to find the frequency functions of some simple functions of this variable. The most important are the first and second order moments in a sample containing a certain number of values of the variable.     

变系数二阶微分方程解的有界性

讨论二阶微分方程x"(t)+p(t)x'(t)+q(t)f(x)=r(t)解的有界性问题,并给出了判定其解有界的方法.     

On the optimum spacing of sample quantiles from a normal distribution. Part I

Abstract

Assume that a large number of observations are made on a normal random variable with the density function where σ σ 0, When the sample is very large the ordinary estimates of µ and a involve considerable computational work. In order to simplify the estimation of µ and/or σ it is sometimes convenient to select a small number of sample quantiles and to use estimates which are linear functions of these sample quantiles, Such a procedure is particularly convenient when the observations occur naturally in order of magnitude, which happens in life testing, for instance, Let      

Simultaneous estimation of the location and scale parameters of the gamma distribution by linear functions of order statistics

Summary

Large sample estimation of the origin (α₁ and the scale parameter (α₂ of the gamma distribution when the shape parameter m is known is considered. Assuming both parameters are unknown, the optimum spacings (0<λ₁<λ₂<...λ _k <1) determining the maximum efficiences among other choices of the same number of observations are obtained. The coefficients to be used in computing the estimates, their variances and their asymptotic relative efficiencies (A.R.E.) relative to the Cramer Rao lower bounds are given.     

Large sample validity of the binomial distribution for lives with unequal mortality rates

Abstract

Let us consider a group of n lives which are observed during some time or age interval. Suppose that the following conditions are satisfied: 1. The probability of death within the interval considered has the same value q for each person of the group.

2. These lives represent statistically independent observations (with respect to mortality).

     

Numerical computation of Theta in a jump-diffusion model by integration by parts

Using the Malliavin calculus in time inhomogeneous jump-diffusion models, we obtain an expression for the sensitivity Theta of an option price (with respect to maturity) as the expectation of the option payoff multiplied by a stochastic weight. This expression is used to design efficient numerical algorithms that are compared with traditional finite-difference methods for the computation of Theta. Our proof can be viewed as a generalization of Dupire's integration by parts to arbitrary and possibly non-smooth payoff functions. In the time homogeneous case, Theta admits an expression from the Black–Scholes PDE in terms of Delta and Gamma but the representation formula obtained in this way is different from ours. Numerical simulations are presented in order to compare the efficiency of the finite-difference and Malliavin methods.     

Applying the method of simulated moments to estimate a small agent-based asset pricing model

The paper takes a recent agent-based asset pricing model by Manzan and Westerhoff from the literature and applies the method of simulated moments to estimate its six parameters. In selecting the moments, the focus is on the fat tails and autocorrelation patterns of the daily returns of several stock market indices and foreign exchange rates. It is argued that it may be meaningful to abandon the econometrically optimal weighting matrix in the objective function and instead invoke the moments' t-statistics in an intuitively appealing way. This modification gives rise to estimations whose moment matching, given the model's parsimony, can be largely considered to be satisfactory. Also the parameter estimates across different markets make good economic sense.     

Risk preferences and the marketing of financial services: Segmentation by birth order

Traditional investment questionnaires may yield an incomplete measure of clients’ risk tolerance. Birth order has the potential to provide additional insight into the true nature of customers’ risk aversion, thereby assisting financial advisors to formulate the optimal investment portfolio for each client. We summarize research findings on birth order-related personality traits that have potential impact on the financial services industry. Marketing implications for investment firms are discussed in a framework that considers customers’ birth order differences in risk tolerance, patience, financial goals and conformity.     

The measurement of the creation and distribution of wealth in a firm by the method of surplus accounts

Within a firm the task of creating wealth through the expansion of the volume of activity and the improvement of productivity is inseparable from the problem of its distribution among all the social partners contributing to the production of that wealth. Therefore, it is useful to analyse both of those aspects within the same conceptual framework. To this end an accounting model is developed in the present study from the basic principles of the “surplus accounts” method. This method has been developed in France over the last few years and it has been tested in several large state-owned companies and in some large and small business firms. The results are generally considered as very encouraging in spite of some conceptual and practical difficulties.     

Estimating continuous-time stochastic volatility models of the short-term interest rate: a comparison of the generalized method of moments and the Kalman filter

This paper examines a model of short-term interest rates that incorporates stochastic volatility as an independent latent factor into the popular continuous-time mean-reverting model of Chan et al. (J Financ 47:1209–1227, 1992). I demonstrate that this two-factor specification can be efficiently estimated within a generalized method of moments (GMM) framework using a judicious choice of moment conditions. The GMM procedure is compared to a Kalman filter estimation approach. Empirical estimation is implemented on US Treasury bill yields using both techniques. A Monte Carlo study of the finite sample performance of the estimators shows that GMM produces more heavily biased estimates than does the Kalman filter, and with generally larger mean squared errors.     

Sequential estimation problems for the scale parameter of a Pareto distribution

Abstract

The Pareto distribution plays a central role in many areas of econometrics. So, we first consider sequential point estimation problems for the scale parameter of a Pareto distribution. Under a very general loss structure, we derive several asymptotic results regarding the associated “risk” and “regret” functions. Then, we consider the problem of constructing a fixed-ratio confidence interval for the scale parameter, and we propose various sampling techniques to achieve the intended goal. Most of our theoretical findings are asymptotic in nature for either problem, and thus we have presented extensive simulation studies to examine moderate sample performances of all the procedures. The findings in the point estimation problem are also supposed to fill many important gaps left in the paper of Wang (1973).     

Judgmental evaluation of sample results: A study of the type and severity of errors made by practicing CPAs

This paper examines the extent to which practicing CPAs may employ two heuristics, representativeness and protectiveness, which lead to systematic errors in the judgement evaluation of sample outcomes. The results indicate that both heuristics are used, but to a lesser extent than suggested by previous research. Implications of the results for audit firm policy are discussed.     

“Every today was a tomorrow”: An integral method for indexing the social mediation of preferred futures

The visions we hold of the future, whether they are of utopias or dystopias, are not simply a matter of personal imagination. Our conceptions of the future are mediated to us as much as they are privately created by us. To this point, futures studies have not developed an integrative and broad-based framework for considering the social mediation of futures. Understanding how social mediation impacts on our futures visioning requires an interpretive framework that can cope with the multilayered nature of futures visions, the worldviews that are associated with them and a theory of mediation that can be applied within such a context of ‘depth’. Using theory-building methodology, the current paper attempts this task by describing a theory of social mediation that builds on the integral futures framework. An application of the framework explores the relationship between various scenarios of health care futures, their associated worldviews and the mediational factors that influence our visions of future health care systems.     

Bidding behavior in the longer term refinancing operations of the European Central Bank: Evidence from a panel sample selection model

This paper analyzes individual bidding data of the longer term refinancing operations (LTROs) of the European Central Bank. We investigate how banks’ bidding behavior is related to a series of exogenous variables including collateral costs, interest rate expectations, market volatility and to individual bank characteristics like country of origin, size, and experience. A specific feature of these auctions is that the number and composition of bidders varies over time. Therefore, we estimate panel sample selection models to control for a bank’s endogenous participation decision. We find that bidding strategies depend on the banks’ attributes. Yet, different bidding behavior generally does not translate into differences concerning bidder success. There is evidence for the winner’s curse effect in LTROs indicating a common value component in banks’ demand for longer term refinancing.     

An assessment of the psychometric properties of the Perceived Stress Scale-10 (PSS10) with a U.S. public accounting sample

Utilizing a convenience sample of 305 professional staff from seven public accounting firms, this study examined: a) the factor structure of the Perceived Stress Scale-10 (PSS10; Cohen & Williamson, 1988); b) the invariance of its factor structure; c) the scale's reliability; and, d) its convergent and divergent validity. Our analyses support a structure with two primary factors, (General Distress and Ability-to-Cope), which load on a single second order factor, Perceived Stress, regardless of gender. Spearman–Brown reliability coefficients, item-total correlations, and coefficient alphas each supported the reliability of the items loading on the full scale as well as on each of the two primary factors. Collectively, these findings provide compelling evidence in support of the PSS10 as a perceived stress measure for accounting professionals. However, more research is warranted to investigate the efficacy of a reduced six-item version of the instrument.     

Impact of US and UK macroeconomic news announcements on the return distribution implied by FTSE-100 index options

This study investigates the effect of scheduled US and UK macroeconomic news announcements on the return distribution implied by FTSE-100 option prices. The results provide new evidence for the whole implied return distribution being systematically affected by certain macroeconomic news announcements. After controlling the unexpected content of the news announcement for quality (good vs. bad news) it is found that good (bad) news causes implied volatility to decrease (increase), option-implied return distribution becomes less (more) left-skewed and kurtosis increases (decreases). The results are consistent with the behavioral model created by Barberis et al. [Barberis, N., Shleifer, A., and Vishny, R. (1998). A model of investor sentiment. Journal of Financial Economics, 49, 307-343.], in which good (bad) news is expected to be followed by good (bad) news.