Negative Exponential Populations Research Articles

Second-order (s.o.) multi-stage fixed-width confidence interval (FWCI) estimation strategies for comparing location parameters from two negative exponential (NE) populations: illustrations with cancer data

Second-order (s.o.) multi-stage fixed-width confidence interval (FWCI) estimation strategies for comparing location parameters from two negative exponential (NE) populations: illustrations with cancer data

The unitary elasticity property in a monocentric city with negative exponential population density

The central prediction of the monocentric city model is that real estate prices, density of development, population density, and land rent decline with the distance from urban center. The spatial pattern follows a negative exponential under the conditions derived by Brueckner (1982) and McDonald and Kim (1987). Research has demonstrated that these exponential density gradients have flattened over time due to rising income and falling transportation costs. This paper identifies a heretofore unknown property in a monocentric city with negative exponential population density, the “unitary elasticity property (UEP).” If a city is characterized by a constant density gradient, even if the slope of that gradient is changing over time, the sum of the elasticity of central density and the elasticity of land area with respect to population change will be approximately equal to unity. When this new prediction is tested, it fits US cities fairly well. Further analysis demonstrates that topographic barriers and age of housing stock are the key factors explaining the deviation from the UEP.

Multistage estimation of the difference of locations of two negative exponential populations under a modified Linex loss function: Real data illustrations from cancer studies and reliability analysis

ABSTRACTWe have designed modified two-stage and purely sequential strategies to estimate the difference of location parameters from two independent negative exponential populations having unknown but proportional scale parameters under a modified Linex loss function. This article extends one-sample methodologies of Mukhopadhyay and Bapat (2016, Sequential Analysis). Some preliminary results are established along the lines of Mukhopadhyay and Hamdy (1984, Canadian Journal of Statistics) and Mukhopadhyay and Darmanto (1988, Sequential Analysis). We have resorted to Mukhopadhyay and Duggan (1997, Sankhya, Series A) in developing asymptotic second-order properties for the modified two-stage methodology and to nonlinear renewal theory of Lai and Siegmund (1977, 1979, Annals of Statistics) and Woodroofe (1977, Annals of Statistics) in addressing analogous properties under the purely sequential methodology. Then, we supplement with extensive sets of data analysis via computer simulations validating that both modified two-stage and purely sequential methods perform very well. Both methodologies are also illustrated and implemented using real datasets from cancer studies and reliability analysis.

On Two-Stage Selection of the Best Negative Exponential Population with Applications

SYNOPTIC ABSTRACTWe revisit the problem of selecting the best among k (≥ 2) independent negative exponential populations, each with unknown location and scale parameters. Thus, we go back to Desu et al.'s (1977) two-stage selection methodology that was developed for the case when the scale parameters were all equal but unknown. That selection methodology is first extended for situations where scale parameters have the form Ciσ with σ(> 0) being unknown but ci(> 0) is known, not all equal, i = 1, …, k(≥ 2). It is shown that this new two-stage selection methodology does not require any new statistical table for its implementation beyond what was required by the original 1977 methodology of Desu et al. We have also addressed the customary sticky problem regarding the choice of an appropriate pilot sample size. Two illustrations are included with the help of real data that came from the area of weed and plant science.

Modèles économétriques des configurations des aires urbaines françaises

Econometric models of spatial urban structure : the case of French metropolitan areas. This paper presents different econometric models that account for the changes or urban spatial structures in France over the last decades. These changes are characterised by a decline of population densities in city centers and by an urban sprawl for population and employment. The monocentric model offers a relevant framework to study household location choices. This model not only identifies some factors that have an impact on these choices but also predicts that population density is represented by a negative exponential function. A two-pronged empirical approach is adopted in this article. We first estimate negative exponential population densities for each of the 112 French metropolitan areas selected from the last four population censuses (1975, 1982, 1990 and 1999). These metropolitan areas count over 8000 communes (commune is the smallest administrative entity in France). Taking the gradient of this negative exponential density function allows to measure patterns of household location over time. Any econometric work based on spatial data needs to take into account spatial interactions among observations and thus to use appropriate econometric tools. Therefore, we estimate two types of spatial econometric specification for this negative exponential density function : a spatial autoregressive model and a spatial error model with two different spatial weight matrices. Estimated spatial model specifications are assessed using different statistical tests such as Lagrange multiplier and Kelejian-Robinson tests. Compared to the conventional ordinary least squares estimation results (with no spatial autocorrelation), estimated spatial models indicate that the estimates of the density gradients and central den¬ sities are lower, hence resulting in a much smoother urban sprawl trend. In the second stage, we introduce in the previous model of population densities additional explanatory variables such as the size of central city area, income and size of households, housing benefits, the infrastructures and natural amenities of the communes. As it was done previously, different spatial models are estimated. Because of technical constraints associated with the econometric procedure, we select two samples of communes, one with communes belonging to small metropolitan areas and one representing communes of great metropolitan areas. The various statistical test results led us to accept a spatial autoregressive model specification with a spatial autocorrelation of errors. Compared to the foregoing econometric results, we can observe that these new estimated models offer a better goodness-of-fit. Furthermore, these additional explanatory variables work either as agglomerative forces or dispersion forces.

Sequential estimation of exponential lacation parameter using an asymmetric loss function

For a two-parameter negative exponential population with both parameters unknown, the bounded risk sequential estimation problem of the location parameter is considered under an asymmetric linex loss funmction. Asymptotic second-order expansion of the risk function is derived for a general class of stopping variables. Some examples are include involving purely scquential and accelerated sequential sampling methodologies. A Monte-Carlo study is carried out to support the asymptotic results and to compare the performance of the different sampling methodologies.

All pairwise comparisons of exponential location parameters under type i censoring — equal scale parameter case

In this paper, procedures for all pairwise comparisons of location parameters of negative exponential populations are developed when the common scale parameter is known or unknown using large sample distributional approximations of the relevant random variables. The small sample performance of these procedures are then examined using Monte Carlo simulation.

Multistage Selection and Ranking Procedures: Second-Order Asymptotics.

Theory of sequential and multistage procedures selecting the best normal population selecting the best negative exponential population estimation of ordered parameters selecting the best component in a multivariate normal population estimation after selection and ranking additional topics notation and abbreviations.

The Effect of Ocean and Lake Coast Amenities on Cities

This article uses census tract data to examine the importance of the role played by coastlines offering city residents recreational enjoyment. A model of an amenity coast city is developed which motivates a restructuring of the negative exponential population density function. The econometric results suggest that the standard urban model of estimating population density is inappropriate for some coastal cities. Instead, distance from census tract to the coast is necessary to attain unbiased population density gradients.

On the admissibility of some sequential confidence intervals for the negative exponential location parameter

With reference to a general class of sequential procedures, this paper shows the admissibility of fixed-width confidence intervals, based on the smallest sample observation, for the location parameter of a negative exponential population with an unknown scale parameter.

Sequential Likelihood Rules for Selecting the Negative Exponential Population Having the Smallest Scale Parameter

We consider k independent two­parameter exponential populations having unknown scale parameters. The problem is to select the popula­tion associated with the smallest scale parameter under Bechhofers (1954) “indifference­zone“ approach. Likelihood based sequential rules are studied when the location parameters are unknown, known, and some known/some unknown. The general methodology has been illustrated extensively, both theoretically and by means of simulated experimunts when k=2,

Point estimation of the largest location of k negative exponential populations

We consider k negative exponential populations having unknown location parameters 01,…,0k with equal but unknown scale parameter σ. Given certain classes of loss functions, our goals have been to construct minimax and bounded maximal risk point estimators for 0∗ = max{01,…,0k}. Various sequential and multistage procedures have been addressed and the maximal risks of the corresponding estimators are presented.

Simultaneous estimation after selection and ranking and other procedures: The negative exponential case

We considerk (≥2) independent negative exponential populations with unknown location parameters and unknown but equal scale parameter. We incorporate the existing purely sequential and three-stage sampling procedures for selecting the “best” population and study the asymptotic second-order characteristics of the proposed fixed-size simultaneous confidence regions for the location parameters constructed after selection and ranking. Some direct estimation procedures have also been discussed.

Fixed Precision Estimation of a Positive Location Parameter of a Negative Exponential Population

Sequential confidence intervals for the positive location parameter of a negative exponential population are studied when the scale parameter is unknown. Since traditional fixed-width confidence intervals here do not lead to satisfactory solutions, we propose a different approach to construct “fixed-precision” confidence intervals for the location. Various asymptotic properties of our confidence interval procedure are discussed briefly.

Fixed-width interval estimation of the largest location of k negative exponential populations

We consider k (≥ 2) negative exponential populations having unknown locations θ1,...,θk, but unknown and equal scale parameter σ. We look at the problem of constructing fixed-width confidence intervals for having the confidence coefficient at least or approximately α which is preassigned. We present various two-stage, sequential and three-stage sampling techniques and discuss several exact and first- as well as second-order asymptotic properties.

Sequential estimation of the difference of means of two negative exponential populations

In this paper, we discuss sequential procedures for estimating the difference of means of two independent negative exponential populations with unknown locations.Up to various orders of approximation, we obtain minimum risk point estimators when the loss function is squared error plus linear cost.We address this problem separately when the scale parameters are (i) unknown but equal and (ii) unknown and unequal.In the first situation, we derive, among other things, asymptotic second order characteristics; while in the second situation, we are able to develop only the first order properties.We also give comments on truly encouraging moderate sample size performances of the proposed sampling procedures.

Sequential estimation problems for negative exponential populations

The literature on sequential estimation problems for negative exponential populations has been reviewed here, We attempt to bring in all the published and unpublished materials known to us in a fairly coherent fashion. Both the concepts and theoretical findings are discussed.

Three-stage estimation procedures for the negative exponential distributions

Fixed-width confidence interval estimation problems for location parameters of negative exponential populations have been studied. Three-stage sampling procedures have been developed for both the one- and two-sample situations. Our discussions are primarily concerned with second-order expansions of various characteristics of the proposed procedures including those for the achieved coverage probability in either problem. Some simulated results are also presented to indicate the usefulness of our procedures for moderate sample sizes.

Two-stage procedures for selecting the best exponential population when the scale parameters are unknown and unequal

In this paper, we discuss two-stage procedures for selecting the largest location parameter among k (≥ 2) negative exponential populations having unknown and unequal scale parameters. We compare this new two-stage procedure for k = 2 with that of Mukhopadhyay (1984), and Mukhopadhyay's (1984) procedure comes out as the inferior one. To facilitate this comparison, we need a specialized table (Table I) for the Studentized smaller Chi-squares, and we provide with an exact method to do just that. The Table I is also very useful for another related problem discussed in Mukhopadhyay and Hamdy (1963). In the end, we present a limited simulation study about the moderate sample-size performances of the two-stage procedures in Mukhopadhyay (1984), and Mukhopadhyay and Hamdy (1983) for k = 2. However, for a general k (≥ 3), our newly developed two-stage procedures as developed here are the only ones known to us at this time.

Estimation of the Mean of a Selected Negative Exponential Population

SUMMARY Let Xi be independent, negative exponentially distributed with unknown expectation λi, i = 1, …, k. Let J and M denote the (random) indices of the maximal and minimal observation, respectively. The paper considers estimation of the random quantities λJ and λM. The loss function is (a – λM)2/λ2 M for λM, and correspondingly for λJ. UMVUE and minimax estimators are shown to exist and are exhibited, and certain other reasonable estimators are discussed.