On the recursive evaluation of a certain multivariate compound distribution

Political scientists often study dollar-denominated outcomes that are zero for some observations. These zeros can arise because the data-generating process is granular: The observed outcome results from aggregation of a small number of discrete projects or grants, each of varying dollar size. This article describes the use of a compound distribution in which each observed outcome is the sum of a Poisson—distributed number of gamma distributed quantities, a special case of the Tweedie distribution. Regression models based on this distribution estimate loglinear marginal effects without either the ad hoc treatment of zeros necessary to use a log-dependent variable regression or the change in quantity of interest necessary to use a tobit or selection model. The compound Poisson—gamma regression is compared with commonly applied approaches in an application to data on high-speed rail grants from the United States federal government to the states, and against simulated data from several data-generating processes.

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On the Use of Recursive Evaluation of Derivatives and Padé Approximation to Solve the Blasius Problem

Journal of Computational Methods in Physics ◽

10.1155/2016/3698251 ◽

2016 ◽

Vol 2016 ◽

pp. 1-5

Author(s):

Asai Asaithambi

Keyword(s):

Differential Equation ◽

Computational Effort ◽

Navier Stokes ◽

Series Solutions ◽

Third Order ◽

Navier Stokes Equation ◽

Order Problem ◽

Algorithmic Differentiation ◽

Blasius Problem ◽

Recursive Evaluation

The Blasius problem is one of the well-known problems in fluid mechanics in the study of boundary layers. It is described by a third-order ordinary differential equation derived from the Navier-Stokes equation by a similarity transformation. Crocco and Wang independently transformed this third-order problem further into a second-order differential equation. Classical series solutions and their Padé approximants have been computed. These solutions however require extensive algebraic manipulations and significant computational effort. In this paper, we present a computational approach using algorithmic differentiation to obtain these series solutions. Our work produces results superior to those reported previously. Additionally, using increased precision in our calculations, we have been able to extend the usefulness of the method beyond limits where previous methods have failed.

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Conversion of Oil Palm Empty Fruit Bunch (EFB) Biomass to Bio-Oil and Jet Bio-Fuel by Catalytic Fast-Pyrolysis Process

ASM Science Journal ◽

10.32802/asmscj.2020.508 ◽

2021 ◽

Vol 14 ◽

pp. 1-11

Author(s):

Haryanti Yahaya ◽

Rozzeta Dollah ◽

Norsahika Mohd Basir ◽

Rohit Karnik ◽

Halimaton Hamdan

Keyword(s):

Oil Palm ◽

Zeolite Y ◽

Fast Pyrolysis ◽

Batch Process ◽

Zeolite Catalysts ◽

Catalyst Loading ◽

Empty Fruit Bunch ◽

Catalytic Fast Pyrolysis ◽

Compound Distribution ◽

Bio Oil

Oil palm empty fruit bunch (EFB) biomass is a potential source of renewable energy. Catalytic fast-pyrolysis batch process was initially performed to convert oil palm EFB into bio-oil, followed by its refinement to jet bio-fuel. Crystalline zeolites A and Y; synthesised from rice husk ash (RHA), were applied as heterogeneous catalysts. The catalytic conversion of oil palm EFB to bio-oil was conducted at a temperature range of 320-400°C with zeolite A catalyst loadings of 0.6 - 3.0 wt%. The zeolite catalysts were characterised by XRD, FTIR and FESEM. The bio-oil and jet bio-fuel products were analysed using GC-MS and FTIR. The batch fast-pyrolysis reaction was optimised at 400°C with a catalyst loading of 1.0 wt%, produced 42.7 wt% yields of liquid bio-oil, 35.4 wt% char and 21.9 wt% gaseous products. Analysis by GCMS indicates the compound distribution of the liquid bio-oil are as follows: hydrocarbons (23%), phenols (61%), carboxylic acids (0.7%), ketones (2.7%), FAME (7.7%) and alcohols (0.8%). Further refinement of the liquid bio-oil by catalytic hydrocracking over zeolite Y produced jet bio-fuel, which contains 63% hydrocarbon compounds (C8-C18) and 16% of phenolic compounds.

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Integral equations for compound distribution functions

Journal of Applied Probability ◽

10.2307/3215062 ◽

1996 ◽

Vol 33 (2) ◽

pp. 388-399 ◽

Cited By ~ 1

Author(s):

Christian Max Møller

Keyword(s):

Point Processes ◽

Marked Point ◽

Building Blocks ◽

Distribution Functions ◽

Jump Processes ◽

Marked Point Processes ◽

Martingale Theory ◽

Compound Distribution ◽

Change Of Variable ◽

Fixed Period

The aim of the present paper is to introduce some techniques, based on the change of variable formula for processes of finite variation, for establishing (integro) differential equations for evaluating the distribution of jump processes for a fixed period of time. This is of interest in insurance mathematics for evaluating the distribution of the total amount of claims occurred over some period of time, and attention will be given to such issues. Firstly we will study some techniques when the process has independent increments, and then a more refined martingale technique is discussed. The building blocks are delivered by the theory of marked point processes and associated martingale theory. A simple numerical example is given.

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