Volterra Integral Equations and Some Nonlinear Integral Equations with Variable Limit of Integration as Generalized Moment Problems

In this paper we will see that, under certain conditions, the techniques of generalized moment problem will apply to numerically solve an Volterra integral equation of first kind or second kind. Volterra integral equation is transformed into a one-dimensional generalized moment problem, and shall apply the moment problem techniques to find a numerical approximation of the solution. Specifically you will see that solving the Volterra integral equation of first kind f（t） = {a^t K（t, s）x（s）ds a ≤ t ≤ b or solve the Volterra integral equation of the second kind x（t） =f（t）＋{a^t K（t,s）x（s）ds a ≤ t ≤ b is equivalent to solving a generalized moment problem of the form un = {a^b gn（s）x（s）ds n = 0,1,2… This shall apply for to find the solution of an integrodifferential equation of the form x＇（t） = f（t） ＋ {a^t K（t,s）x（s）ds for a ≤ t ≤ b and x（a） = a0 Also considering the nonlinear integral equation： f（x）= {fa^x y（x-t）y（t）dt This integral equation is transformed a two-dimensional generalized moment problem. In all cases, we will find an approximated solution and bounds for the error of the estimated solution using the techniques ofgeneralized moment problem.

Solution of Partial Derivative Equations of Poisson and Klein-Gordon with Neumann Conditions as a Generalized Problem of Two-Dimensional Moments

It will be shown that finding solutions from the Poisson and Klein-Gordon equations under Neumann conditions are equivalent to solving an integral equation, which can be treated as a generalized two-dimensional moment problem over a domain that is considered rectangular. The method consists to solve the integral equation numerically using the two-dimensional inverse moments problem techniques. We illustrate the different cases with examples.

Parabolic Partial Differential Equations as Inverse Moments Problem

We considerer parabolic partial differential equations under the conditions on a region . We will see that we can write the equation in partial derivatives as an Fredholm integral equation of first kind and will solve this latter with the techniques of inverse moments problem. We will find an approximated solution and bounds for the error of the estimated solution using the techniques on moments problem. Also we consider the one- dimensional one-phase inverse Stefan problem.

Partial Differential Equations as Three-Dimensional Inverse Problem of Moments

We considerer partial differential equations of second order, for example the Klein-Gordon equation, the Poisson equation, on a region E = （a1, b1 ） × （a2, b2 ） x （a3, b3 ）. We will see that with a common procedure in all cases, we can write the equation in partial derivatives as an Fredholm integral equation of first kind and will solve this latter with the techniques of inverse problem moments. We will find an approximated solution and bounds for the error of the estimated solution using the techniques on problem of moments.

Likelihood Inference under Generalized Hybrid Censoring Scheme with Comp eting Risks

Statistical inference is developed for the analysis of generalized type-Ⅱ hybrid censoring data under exponential competing risks model. In order to solve the problem that approximate methods make unsatisfactory performances in the case of small sample size,we establish the exact conditional distributions of estimators for parameters by conditional moment generating function(CMGF). Furthermore, confidence intervals(CIs) are constructed by exact distributions, approximate distributions as well as bootstrap method respectively,and their performances are evaluated by Monte Carlo simulations. And finally, a real data set is analyzed to illustrate all the methods developed here.

The New Mixed Generalized Erlang Distribution

In probability theory, the mixture distribution M has a density function for the collection of random variables and weighted by wi ≥ 0 and . These mixed distributions are used in various disciplines and aim to enrich the collection distribution to more parameters. A more general mixture is derived by Kadri and Halat, by proving the existence of such mixture by wi ∈ R, and maintaining . Kadri and Halat provided many examples and applications for such new mixed distributions. In this paper, we introduce a new mixed distribution of the Generalized Erlang distribution, which is derived from the Hypoexponential distribution. We characterize this new distribution by deriving simply closed expressions for the related functions of the probability density function, cumulative distribution function, moment generating function, reliability function, hazard function, and moments.

Environmental Regulation,Pollution Treatment Productivity,and Industrial Environmental TFP in China

Amidst growing environmental protection intensity by the Chinese government, this paper investigates the effects of environmental regulation on China＇s industrial pollution treatment productivity and environmental TFP. By estimating China＇s pollution treatment productivity between 2001 and 2008 and analyzing environmental regulation intensity and the effects of the relevant factors and pollution treatment productivity using panel data, this paper discovers that （1） pollution treatment productivity contributed a significant share of about 40% to industrial environmental TFP during the investigation period; （2） environmental regulation may not necessarily cause adverse impacts on pollution treatment efficiency and productivity but demonstrates a U-shaped relationship： when the share of pollution treatment cost in industrial value-added is above the range of 3.8%-5.1%, environmental regulation is likely to promote pollution treatment productivity and thus environmental TFP Judging by the estimation result, enhancing environmental protection and expediting the development of ecological civilization are conducive to China ＂s economic transition towards an intensive, efficient, circular, and sustainable development pattern. China＇s current industrial development has the capacity to tolerate a rather demanding level of pollution treatment and management and China needs to further rely on energy conservation and the environmental production industries to promote the progress of pollution treatment technologies.

MOMENT GENERATING FUNCTIONS OF RANDOM VARIABLES AND ASYMPTOTIC BEHAVIOUR FOR GENERALIZED FELLER OPERATORS

Describes the representation of moment generating function for the S-lambda type random variables. Higher order asymptotic formula for generalized Feller operators; Regular n-r order moment for the random variables.

The mechanism and heterogeneity of environmental regulations'impact on the technological progress of dairy farming

The study analyses the theoretical mechanism through which environmental regulation affects the dairy industry’s technological progress,with a particular focus on how the effect is conditional on farm size.Using the input–output data of dairy farms of different sizes from 2009 to 2019 in 10 Chinese provinces/autonomous regions in China and the quantitative measurement index of environmental regulation,the study estimates environmental regulation’s heterogeneous influences on the dairy industry’s technological progress by dynamic panel data models.The empirical results suggest that,first,environmental regulation has a U-type influence on the technological progress of dairy farming.The U-type influence means moving from pollution control’s high cost and low technology progress to the high profit and high innovation input generated by optimizing the breeding structure.Second,the promotion of dairy farming technology depends on farm size.The effect of environmental regulation on technological progress in moderately large-farms showed a U-type relationship.In contrast,the effect in free-range and large-size dairy farms showed a linear and positive relationship.The government should further strengthen environmental regulation based on advancing moderately large-farms in compliance with market mechanisms in the long run.Particular attention should be paid to the forms of environmental regulation so that dairy cattle breeding technology can break through the inflection point of the“U”curve as soon as possible and ensure the significance of the rising stage.Along the way,technical support should be provided for realizing environmental protection and economic growth.

Financial constraints and investment decisions of listed Indian manufacturing firms

Background:The purpose of the study is to understand the role of cash flow sensitivity to investment as a measure of financial constraints among listed Indian manufacturing firms.It also analyses the role of tangibility in alleviating financial constraints.Further,the role of other financial factors in investment decisions is explored.Methods:The study is conducted using the generalized method of moments(GMM)estimator on dynamic panel data for the period of(2009–2015)on 768 listed manufacturing firms.Results:The analysis finds that cash flow sensitivity is a valid measure of financial constraints in the Indian manufacturing sector.Results according to splitting criteria found that investment decisions of standalone firms are more sensitive to cash flow than group affiliated firms.Further,splitting the firms according to market capitalization and tangible net worth reveals a higher degree of cash flow sensitivity by firms with lower market capitalization and asset tangibility.The results for the effects of tangibility of assets on easing financial constraint were found significant only in the case of firms with low tangible net worth and medium market capitalization.Conclusions:The study confirms cash flow sensitivity to investment as a valid measure of financial constraints.It will confirm pooling of internal funds by financially constrained firms to accept profitable investment opportunities in future.Further,it also reports that asset tangibility eases the financial constraints faced by firms.

Alternative measure of financial development and investment-cash flow sensitivity:evidence from an emerging economy

This study examines the impact of financial development on corporate investment in terms of their influence on financing constraints.This study also tries to find the effect of financial development on the investment-cash flow sensitivity across the size,degree of financial constraints and group affiliation of the firm.This study employs dynamic panel data model or more specifically system generalized method of moments(GMM)estimation technique.The estimation results reveal that cash flow affects the investment decision of the company positively,which implies that Indian firms are financially constrained.Also,we observe that financial development reduces the investment-cash flow sensitivity and the effect of financial development is more prominent for small size and standalone firms.The results are robust across the period and,for both financially constrained and unconstrained firms.This study contributes to the existing literature by analyzing the impact of financial development on the role of cash flow in determining investments undertaken by the Indian firms,which is an unexplored issue from an emerging market perspective.

The Marshall-Olkin Right Truncated Fréchet-Inverted Weibull Distribution: Its Properties and Applications

In this paper, a new probability distribution is proposed by using Marshall and Olkin transformation. Some of its properties such as moments, moment generating function, order statistics and reliability functions are derived. The method of maximum likelihood is used to estimate the model parameters. The graphs of the reliability function and hazard rate function are plotted by taken some values of the parameters. Three real life applications are introduced to compare the behaviour of the new distribution with other distributions.

A Linear Immigration-Birth-Death Model and Its Statistical Inference

formula of simulation proccss by In this paper, we employ monmnt generating function to obtain some exact transition probability of inlmigration-birth-death（IBD） model and discuss the of sample path and statistical inference with complete observations of the IBD the exact transition density formula.

Examination of the poverty-environmental degradation nexus in Sub-Saharan Africa

The relationship between environmental degradation and poverty has increasingly become the focus of national strategic decision-making in recent years.However,despite several theoretical explorations on the nexus,a dearth of empirical literature on the poverty-environmental degradation nexus,specifically on Sub-Saharan Africa(SSA),still exists.In this study,we investigated the poverty-environmental degradation nexus in SSA.We hypothesized that poverty is both a cause and effect of environmental degradation,and this relationship is explained as a vicious cycle.Unlike previous studies,we employed several alternative indicators of environmental degradation to examine the poverty-environmental degradation nexus in this study.We used data from 41 countries of SSA between 1996 and 2019 and employed the generalized method of moments(GMM)approach.The findings suggest a cyclical relationship between poverty and environmental degradation in SSA,which confirms that an increase in poverty leads to an increase in environmental degradation,especially in deforestation and PM2.5 emissions.Similarly,the increase in environmental degradation positively affects poverty in SSA.We also confirmed that exogenous conditioning factors such as population growth rate,education,industrialization,and income inequality,institutional quality indicators such as governance effectiveness,control of corruption,freedom ad civil liberty,and democracy,and endogenous factors including fossil fuel energy use,fuelwood energy use,household health expenditure,infant mortality rate,and agriculture productivity influence the nexus between poverty and environmental degradation.The findings on the relationship between poverty and environmental degradation in SSA are a testimonial evidence that both poverty and environmental degradation are significant issues in SSA.Hence,poverty alleviation policies in SSA should not lead to PM2.5 emissions and deforestation,which may as well force people into a poverty-environmental degradation trap.Instead,poverty reduction policies should simultaneously achieve environmental conservation.

Analysis of asymptotically tight approximation SER for cooperative NOMA systems

The closed-form formula derivation of the power domain cooperative non-orthogonal multiple access(NOMA)system is of great significance for further improving the performance of the system.However,the system performance formulas of the channel capacity and the paired bit error rate pairwise error probability(PEP)are too complicated,which have increased the difficulty in system performance optimization.Therefore,based on the amplify forward(AF)relay cooperative NOMA model,the signal interference noise ratio(SINR)formulas of the two user nodes are constructed.Through the assumption of that,the symbol error rate(SER)of each user is fair,the simplification condition of moment generating function(MGF)with the harmonic mean form is satisfied.Combined with the SER calculation formula of MGF,the system SER asymptotically tight approximation formula with simple structure is derived at high signal-to-noise ratio(SNR).The Monte Carlo simulation results show that,the formula can accurately describe the SER performance of the power domain cooperative NOMA system with the non-ideal successive interference cancellation(SIC)system when SNR is high.Under the condition of certain total power,the optimal power allocation factor is solved in order to minimize the total system SER.

On the Application of Nadarajah Haghighi Gompertz Distribution as a Life Time Distribution

The convolution of Nadarajah-Haghighi-G family of distributions will result into a more flexible distribution (Nadarajah-Haghighi Gompertz distribution) than each of them individually in terms of the estimate of the characteristics in there parameters. The combination was done using Nadarajah-Haghighi (NH) generator. We investigated in the newly developed distribution some basic properties including moment, moment generating function, survival rate function, hazard rate function asymptotic behaviour and estimation of parameters. The proposed model is much more flexible and has a better representation of data than Gompertz distribution and some other model considered. A real data set was used to illustrate the applicability of the new model.

Statistical Properties of The Exponentiated Nakagami Distribution

This paper is an improvement over beta-Nakagami distribution developed by Shittu and Adepoju （2013）. Here we propose the addition of one parameter to the two parameter continuous Nakagami-m distribution （Nakagami, 1960） that was designed for modeling the fading of radio signals. The resulting distribution referred to as Exponentiated Nakagami （ENAK） distribution is a generalization of the classical Nakagami distribution. The statistical properties of the proposed distribution such as moments, moment generating function, the asymptotic behavior among others were investigated. The method of maximum likelihood is used to estimate the model parameters and the observed information matrix is derived. A real data set is used to compare the new model with the class of Nakagami distributions. Our findings showed that the Exponentiated Nakagami distribution is more flexible than beta-Nakagami distribution with better representation and less computational effort.

Impact of macro-fiscal determinants on health financing:empirical evidence from low-and middle-income countries

Background:Health financing is a major challenge in low-and middle-income counties(LMICs)for achieving Universal Health Coverage(UHC).Past studies have argued that the budgetary allocation on health financing depends on macrofiscal policies of an economy such as sustained economic growth and higher revenue mobilization.While the global financial crisis of late 2008 observed a shortage of financial resources in richer countries and adversely affected the health sector.Therefore,this study has examined the impact of macro-fiscal policies on health financing by adopting socioeconomic factors in 85 LMICs for the period 2000 to 2013.Methods:The study has employed the panel System Generalized Method of Moment model that captures the endogeneity problem in the regression estimation by adopting appropriate instrumental variables.Results:The elasticity of public health expenditure(PHE)with respect to macro-fiscal factors varies across LMICs.Tax revenue shows a positive and statistically significant relationship with PHE in full sample,pre-global financial crisis,middle-income,and coefficient value varies from 0.040 to 0.141%.Fiscal deficit and debt services payment shows a negative effect on PHE in full sample,as well as sub-samples and coefficient value,varies from 0.001 to 0.032%.Aging and per capita income show an expected positive relationship with PHE in LIMI countries.Conclusions:Favorable macro-fiscal policies would necessarily raise finance for the health sector development but the prioritization of health budget allocation during the crisis period depends on the nature of tax revenue mobilization and demand for health services.Therefore,the generation of health-specific revenues and effective usage of health budget would probably accelerate the progress towards the achievement of UHC.

Flexible Reduced Logarithmic-Inverse Lomax Distribution with Application for Bladder Cancer

In this paper, a new method for adding parameters to a well-established distribution to obtain more flexible new families of distributions is applied to the inverse Lomax distribution (IFD). This method is known by the flexible reduced logarithmic-X family of distribution (FRL-X). The proposed distribution can be called a flexible reduced logarithmic-inverse Lomax distribution (FRL-IL). The statistical and reliability properties of the proposed models are studied including moments, order statistics, moment generating function, and quantile function. The estimation of the model parameters by maximum likelihood and the observed information matrix are also discussed. In order to assess the potential of the newly created distribution. The extended model is applied to real data and the results are given and compared to other models.

Scenario Generation for Cooling,Heating,and Power Loads Using Generative Moment Matching Networks

Scenario generations of cooling,heating,and power loads are of great significance for the economic operation and stability analysis of integrated energy systems.In this paper,a novel deep generative network is proposed to model cooling,heating,and power load curves based on generative moment matching networks(GMMNs)where an auto-encoder transforms highdimensional load curves into low-dimensional latent variables and the maximum mean discrepancy represents the similarity metrics between the generated samples and the real samples.After training the model,the new scenarios are generated by feeding Gaussian noises to the scenario generator of the GMMN.Unlike the explicit density models,the proposed GMMN does not need to artificially assume the probability distribution of the load curves,which leads to stronger universality.The simulation results show that the GMMN not only fits the probability distribution of multiclass load curves very well,but also accurately captures the shape(e.g.,large peaks,fast ramps,and fluctuation),frequency-domain characteristics,and temporal-spatial correlations of cooling,heating,and power loads.Furthermore,the energy consumption of generated samples closely resembles that of real samples.