He describes such discrete distributions as binomial, Poisson, and logarithmic series
. Then he turns to continuous distributions, among them chi-square, exponential, noncentral F, inverse Gaussian, and bivariate normal.
We have worked with logarithmic series
which is a usual practice to deal with the heteroscedasticity problem of time series.
Johansen cointegration estimation results between logarithmic series
of GDP and S[O.sub.2] emissions Eigenvalue Likelihood 5 Percent 1 Percent Hyphotesized Ratio Critical Value Critical Value No.
Recently, Aghababaei Jazi and Alamatsaz (2010) have studied the stochastic ordering comparison of another known member of the family of generalized power series distributions, i.e., the logarithmic series distribution, with its mixture.
 Aghababaei Jazi M., and Alamatsaz M.H., 2010, "Ordering comparison of logarithmic series random variables with their mixtures", Communication in Statistics: Theory and Methods, 39,1-12.
The Whittaker plot guided us in deciding about the most appropriate species-abundance model fitting (geometric series, logarithmic series, truncated lognormal and broken stick model).
The adopted species-abundance model were the Logarithmic Series ([chi square] = 10.959 < [[chi square].sub.0.05;8] = 15.51) and the truncated lognormal ([chi square] = 0.8733 < [[chi square].sub.0.05;6] = 12.59).
The logarithmic series
fitted better to communities characterized as being influenced by only one or a few determining factors affecting ecological interactions, with a high proportion of species found to be very uncommon (Magurran, 1988).
(9) For Reynolds, logarithmic series "provide a reliable model for accelerating or retarding [formal] dimensions," thus affording him precise control over this aspect of his music.
Reynolds first defines one or more logarithmic series using semi-logarithmic graph paper that features a linear x-axis and a logarithmic y-axis, and enables him to create logarithmic series simply by drawing straight lines of varying slope across the paper; a numerical value derived in this manner corresponds to a sectional duration of that many seconds.
Patil, Some Methods of Estimation for the Logarithmic Series
Distribution, Biometrics 18, 68-75 (1962).
In this paper we revisit the classical species abundance distributions (geometric series, logarithmic series
, log-normal and broken-stick), the neutral and the niche partitioning models.