I have a calender object and it is working fine when i select a date it will shows the data based on our current selections but some date values are missing so i replaced with string like 'no data' now when i select a data it need to show the data based on selections and string as well.
It won't be possible unless you could give them any date between the choosen min/max-date of your calendar - maybe with something like: dual('no data', floor(yearstart(today()))). Otherwise these values belong not to the selection.
Are you really sure that it make sense to display these NULL's (after replacing with any selectable value) in the context of the data which have a date? If so you will need a logic which select/displayed the dates AND the 'no data' - maybe by using a separate calendar-field which triggers the appropriate date-selection in the real field AND makes a toggle-select to the 'no data'. An alternatively could be to use set analysis within the expressions maybe with something like this:
I'm not sure what do you mean with 'proof'. If the replacement of any NULL's aren't within the dataset which the user selects the belonging values/records aren't included - it's just the way Qlik works (intentionally).
Above I showed 3 different ways with which you might bypass the standard-logics. This are replacing the NULL's with an estimated value which is probably between the user-selections or a selection-trigger or with set analysis conditions within the expressions.
And the easiest way would be just to use a listbox as selection-tool instead of a calendar object - the user just selects the wanted dates and the 'no data' ...