{smcl}
{* 24nov2003}{...}
{hline}
help for {hi:qdagum}, {hi:pdagum}, {hi:qgb2}, {hi:pgb2}, {hi:qlogn}, {hi:plogn}, {hi:qsm}, {hi:psm}
{hline}

{title:Distributional diagnostic plots for Dagum, generalized beta (second kind), lognormal and Singh-Maddala distributions}

{p 8 25 2}{cmd:qdagum}{space 1}{it:varname} [{cmd:if} {it:exp}] 
[{cmd:in} {it:range}] [{it:weight}] [{cmd:,}  
{cmd:param(}{it:# # #}{cmd:)} {cmdab:gen:erate(}{it:newvar}{cmd:)} 
{it:common_options} ]

{p 8 25 2}{cmd:pdagum}{space 1}{it:varname} [{cmd:if} {it:exp}]
[{cmd:in} {it:range}] [{it:weight}] [{cmd:,} 
{cmd:param(}{it:# # #}{cmd:)} {cmdab:gen:erate(}{it:newvar1 newvar2}{cmd:)} 
{it:common_options} ]

{p 8 25 2}{cmd:qgb2}{space 3}{it:varname} [{cmd:if} {it:exp}] 
[{cmd:in} {it:range}] [{it:weight}] [{cmd:,}  
{cmd:param(}{it:# # # #}{cmd:)} {cmdab:gen:erate(}{it:newvar}{cmd:)} 
{it:common_options} ]

{p 8 25 2}{cmd:pgb2}{space 3}{it:varname} [{cmd:if} {it:exp}] 
[{cmd:in} {it:range}] [{it:weight}] [{cmd:,}  
{cmd:param(}{it:# # # #}{cmd:)} {cmdab:gen:erate(}{it:newvar1 newvar2}{cmd:)} 
{it:common_options} ]

{p 8 25 2}{cmd:qlogn}{space 2}{it:varname} [{cmd:if} {it:exp}]
[{cmd:in} {it:range}] [{it:weight}] [{cmd:,}  
{cmd:param(}{it:# #}{cmd:)} {cmdab:gen:erate(}{it:newvar}{cmd:)} 
{it:common_options} ]

{p 8 25 2}{cmd:plogn}{space 2}{it:varname} [{cmd:if} {it:exp}]
[{cmd:in} {it:range}] [{it:weight}] [{cmd:,} 
{cmd:param(}{it:# #}{cmd:)} {cmdab:gen:erate(}{it:newvar1 newvar2}{cmd:)} 
{it:common_options} ]

{p 8 25 2}{cmd:qsm}{space 4}{it:varname} [{cmd:if} {it:exp}]
[{cmd:in} {it:range}] [{it:weight}] [{cmd:,} 
{cmd:param(}{it:# # #}{cmd:)} {cmdab:gen:erate(}{it:newvar}{cmd:)} 
{it:common_options} ]

{p 8 25 2}{cmd:psm}{space 4}{it:varname} [{cmd:if} {it:exp}]
[{cmd:in} {it:range}] [{it:weight}] [{cmd:,} 
{cmd:param(}{it:# # #}{cmd:)} {cmdab:gen:erate(}{it:newvar1 newvar2}{cmd:)} 
{it:common_options} ]

{p 4 4 2}
where {it:common_options} are

{p 8 8 2}
{cmd:a(}{it:#}{cmd:)}
{cmdab:g:rid}
{cmd:show(}{it:condition}{cmd:)}
{cmd:rlopts(}{it:cline_options}{cmd:)}
{cmd:plot(}{it:plot}{cmd:)}
{it:scatter_options}
{it:twoway_options}

{p 4 4 2}{cmd:pweight}s, {cmd:fweight}s, {cmd:aweight}s and {cmd:iweight}s 
are allowed; see help {help weights}. 


{title:Description}

{p 4 4 2}
{cmd:qdagum} plots the quantiles of {it:varname} against the quantiles of a
three-parameter Dagum distribution. The parameters {cmd:a}, {cmd:b} and {cmd:p}
are taken by default from {cmd:e(ba)}, {cmd:e(bb)} and {cmd:e(bp)}, which is
where {help dagumfit} puts maximum likelihood estimates of them.

{p 4 4 2}
{cmd:pdagum} produces a probability plot for {it:varname} compared with a
three-parameter Dagum distribution.  The parameters {cmd:a}, {cmd:b} and
{cmd:p} are taken by default from {cmd:e(ba)}, {cmd:e(bb)} and {cmd:e(bp)},
which is where {help dagumfit} puts maximum likelihood estimates of them.

{p 4 4 2}
{cmd:qgb2} plots the quantiles of {it:varname} against the quantiles of a
generalized beta (second kind) distribution. The parameters {cmd:a}, {cmd:b}, 
{cmd:p} and {cmd:q}
are taken by default from {cmd:e(ba)}, {cmd:e(bb)}, {cmd:e(bp)} and {cmd:e(bq)}, 
which is where {help gb2fit} puts maximum likelihood estimates of them.

{p 4 4 2}
{cmd:pgb2} produces a probability plot for {it:varname} compared with a 
generalized beta (second kind) distribution. The parameters {cmd:a}, {cmd:b}, 
{cmd:p} and {cmd:q}
are taken by default from {cmd:e(ba)}, {cmd:e(bb)}, {cmd:e(bp)} and {cmd:e(bq)}, 
which is where {help gb2fit} puts maximum likelihood estimates of them.

{p 4 4 2}
{cmd:qlogn} plots the quantiles of {it:varname} against the quantiles of a
two-parameter lognormal distribution. 
The parameters {cmd:m} and {cmd:v} are taken by default from 
{cmd:e(bm)} and {cmd:e(bv)},
which is where {help lognfit} puts maximum likelihood estimates of them.

{p 4 4 2}{cmd:plogn} produces a probability plot for {it:varname} compared with a
two-parameter lognormal distribution. 
The parameters {cmd:m} and {cmd:v} are taken by default from {cmd:e(bm)} 
and {cmd:e(bv)},
which is where {help lognfit} puts maximum likelihood estimates of them.

{p 4 4 2}
{cmd:qsm} plots the quantiles of {it:varname} against the quantiles of a
three-parameter Singh-Maddala distribution. 
The parameters {cmd:a}, {cmd:b} and
{cmd:q} are taken by default from {cmd:e(ba)}, {cmd:e(bb)} and {cmd:e(bq)},
which is where {help smfit} puts maximum likelihood estimates of them.

{p 4 4 2}{cmd:psm} produces a probability plot for {it:varname} compared with a
three-parameter Singh-Maddala distribution. 
The parameters {cmd:a}, {cmd:b} and
{cmd:q} are taken by default from {cmd:e(ba)}, {cmd:e(bb)} and {cmd:e(bq)},
which is where {help smfit} puts maximum likelihood estimates of them.


{title:Remarks} 

{p 4 4 2}In the majority of cases, 
*{cmd:dagum} 
or *{cmd:gb2}
or *{cmd:logn} 
or *{cmd:sm} 
will be used just after 
{cmd:dagumfit}, 
{cmd:gb2fit}, 
{cmd:lognfit} 
or {cmd:smfit} respectively.  
Care should be taken to echo any {cmd:if} or {cmd:in}
restrictions and specification of weights used in setting up the estimation
problem. However, see also the {cmd:param()} and {cmd:show()} options. 


{title:Options}

{p 4 8 2}{cmd:param()} may be used to supply 
parameter values directly for use in comparing observed and fitted values. 
{cmd:a}, {cmd:b} and {cmd:p}, in the case of a Dagum distribution, or 
{cmd:a}, {cmd:b}, {cmd:p} and {cmd:q}, in the case of a generalized beta 
(second kind) distribution, or
{cmd:m} and {cmd:v}, in the case of a lognormal distribution,
or {cmd:a}, {cmd:b} and {cmd:q}, in the case of a Singh-Maddala distribution, 
should be provided as separate values in precisely that order. The 
documentation for {help dagumfit}, {help gb2fit}, {help lognfit} and 
{help smfit} provides details on parameterisation. 

{p 4 8 2}{cmd:generate()} specifies either the name of one new variable or the
names of two new variables to hold the data plotted.  In the case of the 
{cmd:q}* commands here, one new variable generated will hold
the quantiles of the fitted distribution.  In the case of the {cmd:p}*  
commands here, two new variables generated will hold, first, the
distribution function of the specified distribution given parameters and
observed values and, second, the empirical cumulative distribution function. 

{p 4 8 2}{it:common_options} are
{cmd:a(}{it:#}{cmd:)}
{cmdab:g:rid}
{cmd:show(}{it:condition}{cmd:)}
{cmd:rlopts(}{it:cline_options}{cmd:)},
{cmd:plot(}{it:plot}{cmd:)},
{it:scatter_options}, and
{it:twoway_options}.

{p 4 8 2}{cmd:a()} specifies {it:a} in the formula for plotting position.  The
plotting positions are ({it:i} - {it:a}) / ({it:n} - 2{it:a} + 1) for values 
ranked smallest to largest and assigned unique ranks {it:i} = 1, ..., {it:n}. 
The default is {it:a} = 0.5, giving ({it:i} - 0.5) / {it:n}.  
Other choices include {it:a} = 0, giving {it:i} /
({it:n} + 1), and {it:a} = 1/3, giving ({it:i} - 1/3) / ({it:n} + 1/3).

{p 4 8 2}{cmd:grid} adds grid lines at the .05, .10, .25, .50, .75, .90, and
.95 quantiles when specified with any {cmd:q}* command here. 
{cmd:grid} is equivalent to {cmd:yla(0(.25)1, grid) xla(0(.25)1, grid)}
when specified with any {cmd:p}* command here. 

{p 4 8 2}{cmd:show()} may be used to specify 
that you wish to restrict the graph according to some condition, say 
looking at one tail of the distribution only. Note that {cmd:if} 
and {cmd:in} should not be used for this purpose.

{p 4 8 2}
{cmd:rlopts(}{it:cline_options}{cmd:)} affect the rendition of the reference
line; see help {help cline_options}.

{p 4 8 2}
{cmd:plot(}{it:plot}{cmd:)} provides a way to add other plots to the generated
graph; see help {help plot_option}.

{p 4 8 2}
{it:scatter_options} affect the rendition of the plotted points; see help
{help scatter}.

{p 4 8 2}
{it:twoway_options} are any of the options documented in help
{help twoway_options} excluding {cmd:by()}.  These include options for titling
the graph (see help {help title_options}) and options for saving the graph to
disk (see help {help saving_option}).


{title:Examples}

{p 4 8 2}{cmd:. dagumfit income}

{p 4 8 2}{cmd:. qdagum income} 

{p 4 8 2}{cmd:. qdagum income, show(income < 20000)} 

{p 4 8 2}{cmd:. pdagum income} 

{p 4 8 2}{cmd:. qlogn mpg, param(3 .25)} 
        

{title:Author}

{p 4 4 2}Nicholas J. Cox, University of Durham, U.K.{break} 
n.j.cox@durham.ac.uk


{title:Also see}

{p 4 13 2}
Online:  help for {help dagumfit}, {help gb2fit}, {help lognfit}, {help graph}, {help diagplots}