In regression analysis we consider a large number of parameters to limited size data and nobody bothers about it.Why so much concern when a distribution contains three shape parameters?.The larger question in both cases is how successfully we can deal with the estimation problem

I want to add one thing here; I read few papers of some famous researchers’. Authors induct parameters and show the model is a good fit by using the goodness of fit measures i.e. AIC, BIC, etc. But the difference is very small like (AIC; Model A= 294.6, Model B= 295.7: BIC; Model A= 305.0, Model=303.5). So it’s a good thing to add more parameters just for a slight difference??

I believe there is a need to concentrate on the practical utilization of existing distribution along generation of new families of distribution

I agree with Ahsan ul Haq comments. Good points. Thanks.

We are doing (most of the cases) for our livelihood, otherwise we will not get promotion, grants etc. etc...

Thanks All. I'm just user of the software, and have found that the estimation of parameters for newly developed models is a very difficult job by any method like method of moments, MLE, etc., because of too many parameters (4 or more than 4).

People write their own program in R, which is very difficult. In my knowledge, no software (such as Maple, MATLAB, Mathematica, C++, EasyFit, etc.) has this feature.

It would be tremendous if an built-in tool set is developed in the above software to test new Models with Parameter Estimation. The users just need to put their models in the software to test the applicability of their newly developed models with too many parameters and get their results along with the parameter estimation, etc. May be, Newton-Raphson Method of Solving Non-linear Equations, Numerical Quadrature, Programming, etc., will be helpful. It will then enhance its utility and it can compete very well with all other software. In my opinion, we need to take the help of Numerical Analysis and Programming Experts.

Hope the above helps.

Please acknowledge.

Kind regards,

Dr. M. Shakil

Dear All, Thanks, Prof. Dr. Tahir. I agree with your comments which are essential for the users of any software to test their new probability models with too many parameters, say 4, 5, etc. That is, as given below.

(i) Many researchers (including me) are developing new probability models (both continuous & discrete) by using different techniques, e.g., generalized Pearson differential equation, product, sum & ratio of independent random variables, etc., which involve too many parameters, say, 4 or more. Now, the question is to estimate the parameters by different techniques of numerical analysis (namely, Newton-Raphson method, Numerical Quadrature, etc.), which is difficult analytically due to the system of many non-linear equations involving too many parameters obtained through MOM, MLE, etc. Then the question is how to fit these models to the data which may be right-skewed, left-skewed, etc.?

(ii) Based on the above, the users should be able to specify the PDF, CDF, with too many parameters, say 4, 5, etc. in any software, and have a choice of built-in estimation algorithms, so that the users could experiment their models by fitting to the data and compare the results, e.g., by using estimation of parameters, descriptive statistics, superimposition of pdf graphs on the histograms, percentage points, etc.

(iii) I'm sure if we are successful in developing and incorporating the above in Eany software, it will be tremendous, and it can compete with other software, which do not have these features. May be we can integrate "R", "C++", Maple, Mathematica, Matlab, Easyfit, etc., for this purpose.

Hope the above helps in developing a New, Versatile, Efficient Version of any software soon.

Please acknowledge.

Kind regards,

Dr. M. Shakil

In regression analysis we consider a large number of parameters to limited size data and nobody bothers about it.Why so much concern when a distribution contains three shape parameters?.The larger question in both cases is how successfully we can deal with the estimation problem

Dear All

Many thanks for your constructive comments. About new families with 2-3 additional parameters, I think some of them are a bit better than know G-classes like exp-G, beta-G, kw-G, Marshal-olkin G and McDonaldG. I did same papers, but some of new family has great flexibility and I think they are better than known familes, for example Odd log-logistic extension are nice. I and my co-authors are working on some extension of OLL-G was introduced by Gleaton and Lynch (2006). Please see some published  work on OLL-G extensions and check the ability of these distributions to real data..

1)Odd Burr Generalized Family of Distributions with Some Applications

2)The Odd Log-Logistic Lindley Poisson Model for Lifetime Data

3)The odd log-logistic generalized half-normal lifetime distribution: properties and applications

4)A New Log-Location Regression Model: Estimation, Influence Diagnostics and Residual Analysis

5)The Zografos-Balakrishnan odd log-logistic family of distributions: Properties and Applications

6)The Beta Odd Log-Logistic Generalized Family of Distributions

7)A new family of distributions: the Kumaraswamy

odd log-logistic, properties and applications

For estimating the parameters of the distribution we can use easily AdequacyModel or fitdistrplus in R software.

Finally, I want to say that we will give some new families with more flexibility to modeling various type of data sets.

Best regards

I think that the generalized families with more than two parameters are not new, see, McDonald-G by Alexander et al. (2012). My recent paper with Professor Saralees Nadarajah entitled "The beta transmuted-H family for lifetime data" provides three shape parameters. In this paper, we obtain good results for the estimates and for the finite sample performance of the estimators using

simulation.

I think that the attention should also be directed to practical side.

As long as parameter estimation is  addressed where is the problem of having more parameter as said by Nair. Another thing that need to be looked in to is interpreting the parameters!

its a developing world you can not discard some thing saying its complex may with better technology these so called many parameter issue will be just elementary.