A note on the extension of tables for the Friedman statistic

Abstract  The tables for the Friedman rank-test arc extended using a sampling method. A table is given for the traditional significance levels .01, .025, .05 and .10 for number of blocks equal to 7 and 8 and for treatments of size 6 and 7. A brief discussion of available tables is also included along with an example of an application.     

Exceptional Convergence of the Sample Variance

The case is investigated when Hoeffding's one sample U–statistic theorem for the sample variance S² is not applicable. It is shown that this occurs only when the parent distribution is the two–point distribution with jumps of equal magnitude. For this exceptional case the standardised S² is shown to converge in distribution to (1 – V )√2, where V has chi–square distribution with one degree of freedom.     

Exact finite sample properties of double k-class estimators in simultaneous equations

In our earlier paper [Srivastava, Agnihotri and Dwivedi (1980)] the dominance of double k-class over k-class with respect to exact mean squared error matrix criteria is established. It is observed that given a member of k-class, one can pick up a member of double k-class that will provide an improved estimator of the coefficients. This result prompted us to study the exact finite sample properties of the double k-class estimator. For this, we have considered a structural equation containing two endogenous variables and have investigated the properties of double k-class estimators of the coefficients of explanatory endogenous variables assuming characterizing scalars to be non-stochastic.     

A probability inequality for ranges and its application to maximum range test procedures

Summary It is proved that for any fixed argument the sequence (P _k) of the distribution functions of the ranges ofk i.i.d. univariate random variables is log-concave if the random variables have a log-concave density. If the support of the distribution is an infinite interval and the density is monotonous then the theorem holds also with “log-convex” instead of “log-concave”. The resulting inequalities can be used by a quick algorithm for closed maximum range test procedures for all pairwise comparisons (Royen 1988, 1989a, 1989b). Under the above assumptions the application of this algorithm can be extended e.g. to pairwise comparisons of variances.     

Aggregation effects on price and expenditure elasticities in a quadratic almost ideal demand system

Abstract.  While it is well known that demand elasticities calculated at the macro level will in general differ from those calculated at the micro level because of aggregation effects, there remain the questions of how large the effects are and how they vary with the degree of inequality in the income distribution. We explore these questions with models based on a quadratic version of the Almost Ideal Demand System. We investigate the elasticity differences theoretically and then calibrate the models and generate numerical results, using income data for seven countries with widely different distributions. The aggregation effects are found generally to be rather small, even with highly unequal income distributions.     

Dynamic effects of externalities,optimal saving and economic growth

Conclusion Recognizing the fact that provision of mixed public goods can result in both consumption externalities of the Samuelsonian variety as well as production externalities we set out to extend the earlier results of Rao and Kalpagam (1977) on the effect of public goods on economic growth. In so doing, we considered three standard specifications of production externalities and enlarged the concept of consumption displacement. Our basic conclusion is that the results of our earlier paper remain valid under the more general conditions set out in this paper.     

Energy savings by reduced mixing in aeration tanks: results from a full scale investigation and long term implementation at Avedoere wastewater treatment plant

The aim of this project was to investigate the potential of reducing number of mixers in the biological treatment process and thereby achieve energy and economical savings and contribute to cleaner environment. The project was carried out at Avedoere wastewater treatment plant and a full scale investigation was conducted to study the effect of reduced mixing on flow velocity, suspended solid sedimentation, concentration gradients of oxygen and SS with depth and treatment efficiency. The only negative effect observed was on flow velocity; however the velocity was above the critical velocity. The plant has been operating with 50% of its designed number of mixers since September 2007 and long term results also confirm that reduced mixing did not have any negative effect on treatment efficiency. The estimated yearly electricity saving is 0.75 GWh/year.     

The fate of 14C-radiolabelled diclofenac and 4'-hydroxydiclofenac in membrane bioreactor treatment of wastewater

This study aimed at enhancing knowledge on the fate of diclofenac (DF), together with its main human metabolite 4'-hydroxydiclofenac (4'OHDF), during wastewater treatment by using a laboratory-scale membrane bioreactor (MBR). The reactor was fed continuously with non-radiolabelled diclofenac for a one month period prior to a single pulse of a 14C-radiolabelled solution of DF and 4'OHDF. The solution spike contained approximately 25% 4'OHDF and 65% DF, which corresponds to the ratio observed in municipal sewage, as well as traces of two other metabolites. The radioactivity was monitored for a total of twelve days in the various output streams. The calculation of the complete mass balance in the system demonstrated that the major part of the radioactivity left the reactor with the permeate (88.7%), while 2.1% was recovered in the excess sludge. Negligible amounts were recovered in the off-gas traps and on the membranes. Chromatographic analyses of effluent samples, by means of HPLC-MS coupled in parallel to a radiodetector, displayed a different pattern than the one of the spiked solution. It showed the occurrence of three additional metabolites.